55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points."

Transcription

1 Geometry Core Semester 1 Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which topics you need to review most carefully. The unit diagnostics are particularly helpful because they are a form of "pretest" that you can use to assess your performance and prescribe topics for review. Study the unit wrap-ups. Read each unit wrap-up to determine which topics you need to review further. Review important vocabulary terms. Study the key terms listed on the next page to identify any vocabulary you don't know. Use the "Check Your Understanding" pages and math workbook assignments as study aids. Review the "Check Your Understanding" pages to get right, wrong, and hint feedback to specific math problems. The math workbook assignments you've completed throughout the semester will also provide you with a great review for the exam. Review the activities that contain information you need to review further. After determining which topics are least familiar to you, review the activity in which they are covered. This could include revisiting study activities and rereading math workbook assignments. Taking the Semester Exam For all exam questions Read the entire question and all the choices before selecting an answer. Then choose the best answer or answers. Semester Exam 55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points. Semester Review: Geometry, Semester 1

2 Semester Key Terms right triangle right triangle AA similarity postulate AAS theorem acute angle acute triangle altitude angle angle bisector angle bisector theorem angle measure ASA postulate base base angles bisector centroid circumcenter closed figure collinear conditional congruence transformations congruent coplanar corollary cosine cross product property deduction equilateral triangle exterior angle extremes HA theorem HL theorem hypotenuse included angle included side indirect proof induction interior angle isosceles triangle LA theorem legs length line LL theorem means median midpoint obtuse angle obtuse triangle opposite angle opposite side orthocenter parallel lines pattern perpendicular bisector theorem perpendicular lines plane point proof by contradiction proportions protractor Pythagorean theorem Pythagorean triple ratios ray remote interior angle right angle right triangle SAS postulate scale factor scalene triangle segment side similar sine skew lines SSS postulate SSS similarity theorem straight angle syllogism tangent transversal Venn diagram vertex vertical angles zero angle

3 Key Terms and Concepts for Unit 1 Unit 1 Key Terms angle conjecture contrapositive converse corollary deduction definition indirect proof induction inverse postulate proof by contradiction scientific method segment side Venn diagram vertex Know that to use induction, you look for a pattern in what you know and make a conjecture about what you don t know. Know that to use deduction, you use general rules that are certainly true and use them to find particular facts. Know that conditional statements have two parts, an "if" clause and a "then" clause. They are also called "if-then" statements. Know that conditional statements can be illustrated using Venn diagrams and know how to interpret them. The Venn diagram below illustrates the statement "If a thing is a baseball cap, then it is a hat." Know that the converse of "If a, then b" is "If b, then a." Know that the inverse of "If a, then b" is "If not a, then not b." Know that the contrapositive of "If a, then b" is "If not b, then not a."

4 Know that if the statement "If a, then b" is true, then its contrapositive "If not b, then not a" is also true. The converse and inverse are not necessarily true. Know the shorthand for conditional statements: If a, then b If not a, then not b Know how to use syllogisms. The chain of statements below shows how to form a syllogism from two conditionals. Given the statements: If a, then b If b, then c You can conclude: If a, then c Know that a definition is the precise statement of the qualities of an idea, object, or process. Know that a postulate or axiom is a statement that is assumed to be true without proof. Know how to write a two-column proof. The first column contains deductive steps. The second column contains your reasons. Know how to write and understand a proof by contradiction, or an indirect proof. Start by assuming the opposite of what you want to prove and then deduce an impossible statement. Example Make a syllogism from the following statements: If there is cheese in the circus tent, then there are mice in the circus tent. If there are mice in the circus tent, then the elephants are nervous. Then write the contrapositive of the syllogism. Answer Syllogism: If there is cheese in the circus tent, then the elephants are nervous. Contrapositive: If the elephants are not nervous, then there is no cheese in the circus tent.

5 Key Terms and Concepts for Unit 2 Unit 2 Key Terms acute angle angle bisector collinear congruent coplanar length line midpoint perpendicular lines plane point protractor ray segment straight angle zero angle Know that a point has no size. A segment has no width but has finite length. A ray has no width and infinite length in one direction. A line has no width and infinite length in both directions. Know that a segment is named by its endpoints. Know that the length of a segment is written AB. Know that if the point C lies on the segment, then the sum of the lengths of and is equal to the length of. That is, AC + CB = AB. Know that a ray is named by its endpoint and another point on the ray. The endpoint comes first in the name; the other point comes second.

6 . Know that a line is named by two points on the line. or Know that the rays that form an angle are called the sides of the angle, and the point where they meet is called the vertex of the angle. Know that an angle whose sides make a line is called a straight angle. An angle whose sides overlap to make a ray is called a zero angle. Know how to use a protractor. Review Unit 2, Activity 4 for instructions and to practice using a protractor. Know that an acute angle is an angle whose measure is greater than 0 and less than 90. An obtuse angle is an angle whose measure is greater than 90 and less than 180. A right angle is an angle whose measure is exactly 90. Know that adjacent angles share a side and vertex. and are adjacent angles.

7 Know that the bisector of an angle is a ray that divides it into two angles of equal measure. is congruent to. is the bisector of. Know that a linear pair is a pair of adjacent angles that combine to form a straight angle. The angles of a linear pair are supplementary. The measures of supplementary angles add up to 180. and make a linear pair. They are supplementary. Know that complementary angles are angles whose measures add up to 90. and are complementary. Know that two segments are congruent if they have the same length. means that is congruent to. Know that two angles are congruent if they have the same measure. is equal to only if they are the same angle; is congruent to if they have the same measure. means that is congruent to.

8 Example is the bisector of. If = 24, what is? Tip It may help to sketch a diagram of the angles. Answer = 24 Worked-Out Solution Since is the bisector of, you know that. Hence = = 24. Know that if the point M is on and, then M is the midpoint of. Know that two points are collinear if they lie on the same line. Objects (including points) are coplanar if they lie in the same plane. Know that if A and B are contained in a plane, then is entirely contained in the plane. Know that vertical angles are congruent. Know that adjacent angles formed by intersecting lines make linear pairs. Know that perpendicular lines are lines that intersect at right angles. Know that the distance between a line and a point not on the line is the length of the segment that joins the point to the line and is perpendicular to the line. Know that the perpendicular bisector of a segment is the line that passes through the midpoint of the segment and is perpendicular to the segment. Know that skew lines are lines that are not coplanar. (Remember that any one line lies in an infinite number of planes; just because two lines lie in different planes doesn t mean that they are skew they are skew if there is no plane that they both lie in.) Know that parallel lines are coplanar lines that never intersect. Know that given a line and a point P not on, there is one and only one line parallel to that passes through P. Know that a transversal is a line that crosses (or "cuts") two parallel lines.

9 (Theorem) Know that for parallel lines cut by a transversal, corresponding angles are congruent. (Theorem) Know that for parallel lines cut by a transversal, alternate interior angles are congruent. (Theorem) Know that for parallel lines cut by a transversal, consecutive interior angles are supplementary.

10 Example What is the measure of? Answer Worked-Out Solution and the angle with measure 118 are consecutive interior angles, which means they are supplementary. So.

11 Key Terms and Concepts for Unit 3 Unit 3 Key Terms AA similarity postulate AAS theorem ASA postulate centroid circumcenter closed figure congruence transformations cross product property exterior angle extremes incenter included angle included side means medians opposite angle opposite side orthocenter proportion remote interior angle SAS postulate scale factor similar triangles SSS postulate SSS similarity theorem (Definition) Know that a triangle is a closed figure formed by three segments connecting three noncollinear points. The three segments are its sides, and the three points are its vertices. (Theorem) Know that the sum of the measures of a triangle s angles is always 180. If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are also congruent ( A + B + m = 180 and A + B + n = 180, so m = A - B = n ). (Definition) Know that an exterior angle is an angle that forms a linear pair with one of the interior angles of the triangle. is an exterior angle of.

12 (Definition) Know that a remote interior angle is an angle in a triangle that is not adjacent to a given exterior angle. and are the remote interior angles of. (Theorem) Know that the measure of an exterior angle of a triangle equals the sum of the measures of its two remote interior angles. The measure of an exterior angle is always greater than the measure of either of its remote interior angles. (Definition) Know that actions that you can do to a triangle that do not change its size or shape are called congruence transformations and that the three congruence transformations are translating, rotating, and reflecting. (Definition) Know that congruent triangles are triangles whose corresponding parts are congruent. (The definition of congruent triangles is often abbreviated CPCTC: "corresponding parts of congruent triangles are congruent.") Therefore: correspond.. The letters in the triangles names should be ordered to show how the vertices (Theorem) Know that congruence of triangles is reflexive, symmetric, and transitive: Reflexive property: Every triangle is congruent to itself. Symmetric property: If, then. Transitive property: If and, then.

13 (Postulate) Know that if the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. This is called the SSS postulate. (Postulate) Know that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. This is called the SAS postulate. (Postulate) Know that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. This is called the ASA postulate. (Theorem) Know that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another, then the triangles are congruent. This is called the AAS theorem. Know that SSA (side-side-angle congruence) does not guarantee congruent triangles, and AAA (angle-angle-angle congruence) also does not guarantee congruent triangles. (Definition) Know that similar triangles are triangles whose corresponding angles are congruent and whose corresponding sides are proportional in length. (Definition) Know that a ratio is the relation between two quantities expressed as the quotient of one divided by the other. The ratio of a to b is. (Definition) Know that the ratio of the corresponding sides of similar triangles is called the scale factor. (Definition) Know that a proportion is an equation that states that two ratios are equal. is a proportion. The values a and d are called the extremes of the proportion; b and c are called the means. Know that the product of the extremes equals the product of the means. That is, if ad = bc., then This is called the cross product property.

14 Example Given that and are similar, fill in the blanks. Answer and Worked-Out Solution Since and are corresponding sides and AB is three times DE, and since the corresponding sides of similar triangles are proportional, you know that every side of is three times the corresponding side of. Since,. Since,. (Postulate) Know that if two angles of one triangle are congruent to two angles of a second triangle, then the triangles are similar. This is called the AA similarity postulate. (Theorem) Know that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. This is called the SSS similarity theorem. (Theorem) Know that if an angle of one triangle is congruent to an angle of another triangle and if the lengths of the sides including these angles are proportional, then the triangles are similar. This is called the SAS similarity theorem. (Theorem) Know that if two sides of a triangle are congruent, then the angles opposite those sides are congruent. This is called the isosceles triangle theorem. (Theorem) Know that if two angles of a triangle are congruent, then the sides opposite those angles are congruent. A corollary is that equilateral triangles are also equiangular, and vice versa. Another corollary is that each angle of an equilateral triangle measures 60. (Theorem) Know that the longest side of a triangle is always opposite the angle with the largest measure. The shortest side of a triangle is always opposite the angle with the smallest measure.

15 (Definition) Know that a median of a triangle is a line or segment that passes through a vertex and bisects the side opposite that vertex. The medians are shown for the triangle above. (Theorem) Know that the medians of a triangle share a common point of intersection. The point is called the centroid. (Definition) Know that an altitude of a triangle is a line or segment through a vertex and perpendicular to the line containing the opposite side. The altitudes are shown for the triangle above. (Theorem) The altitudes of a triangle share a common point of intersection. The point is called the triangle s orthocenter. The angle bisectors are shown for the triangle above. The angle bisectors of a triangle are the bisectors of the triangle s angles. See the definition for the bisector of an angle above.

16 (Theorem) The angle bisectors of a triangle share a common point of intersection. The point is called the triangle s incenter. The perpendicular bisectors are shown for the triangle above. The perpendicular bisectors of a triangle are the perpendicular bisectors of its sides. See the definition for the perpendicular bisector of a line above. (Theorem) Know that the perpendicular bisectors of a triangle share a common point of intersection. The point is called the circumcenter.

17 Key Terms and Concepts for Unit 4 Unit 4 Key Terms triangle triangle angle bisector theorem area cosine HA theorem HL theorem LA theorem LL theorem perpendicular bisector theorem Pythagorean theorem Pythagorean triple sine tangent trigonometric ratios (Definition) Know that the area of a polygon is the number of square units contained in its interior. The formula for the area of a rectangle with height a and base length b is area = b h. The formula for the area of a triangle is area = altitude perpendicular to the base.). (The height is always the length of the (Theorem) Know that in a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. This is called the Pythagorean theorem. (Theorem: converse of the Pythagorean theorem) Know that if the sum of the squares of the measures of two shorter sides of a triangle equals the square of the longest side, then the triangle is a right triangle. (Definition) Know that a Pythagorean triple is a set of three whole numbers a, b, and c that satisfy the equation a 2 + b 2 = c 2. (Theorem) Know that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. This is called the HL theorem. (Theorem) Know that if the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent. This is called the LL theorem.

18 Example What is the measure of below? Answer Worked-Out Solution By the LL theorem, the two triangles are congruent. 67 in the other triangle, so by CPCT you know that. corresponds to the angle with measure (Theorem) Know that if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the triangles are congruent. This is called the HA theorem. (Theorem) Know that if one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent. This is called the LA theorem. (Theorem) Know that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. This is called the perpendicular bisector theorem. (Theorem) Know that if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. This is called the angle bisector theorem. (Theorem) Know that if a point is in the interior of an angle and equidistant from the two sides of the angle, then it lies on the bisector of the angle. This is the converse of the angle bisector theorem. (Theorem) Know that if the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two triangles formed are similar to the given triangle and to each other. (Theorem) Know that if the length of one leg of a triangle is s, then the length of the other leg is s and the length of the hypotenuse is.

19 Example What is the length of the hypotenuse of this triangle? Answer 2 (Theorem) Know that if the length of the short leg of a triangle is s, then the length of the other leg is and the length of the hypotenuse is 2s. The following are the Trigonometric ratios: (Definition) Know that the sine of an angle is the ratio of the opposite leg length to the hypotenuse length. (Definition) Know that the cosine of an angle is the ratio of the adjacent leg length to the hypotenuse length. (Definition) Know that the tangent of an angle is the ratio of the opposite leg length to the adjacent leg length. Copyright 2012 Apex Learning Inc. (See Terms of Use at

Chapter 1: Essentials of Geometry

Chapter 1: Essentials of Geometry Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,

More information

GEOMETRY CONCEPT MAP. Suggested Sequence:

GEOMETRY CONCEPT MAP. Suggested Sequence: CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons

More information

Geometry Course Summary Department: Math. Semester 1

Geometry Course Summary Department: Math. Semester 1 Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give

More information

Definitions, Postulates and Theorems

Definitions, Postulates and Theorems Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven

More information

#2. Isosceles Triangle Theorem says that If a triangle is isosceles, then its BASE ANGLES are congruent.

#2. Isosceles Triangle Theorem says that If a triangle is isosceles, then its BASE ANGLES are congruent. 1 Geometry Proofs Reference Sheet Here are some of the properties that we might use in our proofs today: #1. Definition of Isosceles Triangle says that If a triangle is isosceles then TWO or more sides

More information

INDEX. Arc Addition Postulate,

INDEX. Arc Addition Postulate, # 30-60 right triangle, 441-442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent

More information

Geometry Chapter 1 Vocabulary. coordinate - The real number that corresponds to a point on a line.

Geometry Chapter 1 Vocabulary. coordinate - The real number that corresponds to a point on a line. Chapter 1 Vocabulary coordinate - The real number that corresponds to a point on a line. point - Has no dimension. It is usually represented by a small dot. bisect - To divide into two congruent parts.

More information

BASIC GEOMETRY GLOSSARY

BASIC GEOMETRY GLOSSARY BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that

More information

Conjectures. Chapter 2. Chapter 3

Conjectures. Chapter 2. Chapter 3 Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical

More information

DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.

DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle. DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent

More information

POTENTIAL REASONS: Definition of Congruence:

POTENTIAL REASONS: Definition of Congruence: Sec 6 CC Geometry Triangle Pros Name: POTENTIAL REASONS: Definition Congruence: Having the exact same size and shape and there by having the exact same measures. Definition Midpoint: The point that divides

More information

of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.

of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent. 2901 Clint Moore Road #319, Boca Raton, FL 33496 Office: (561) 459-2058 Mobile: (949) 510-8153 Email: HappyFunMathTutor@gmail.com www.happyfunmathtutor.com GEOMETRY THEORUMS AND POSTULATES GEOMETRY POSTULATES:

More information

Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles

Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles IMPORTANT TERMS AND DEFINITIONS parallelogram rectangle square rhombus A quadrilateral is a polygon that has four sides. A parallelogram is

More information

Conjectures for Geometry for Math 70 By I. L. Tse

Conjectures for Geometry for Math 70 By I. L. Tse Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:

More information

Triangle congruence can be proved by: SAS. Identify the congruence theorem or postulate:

Triangle congruence can be proved by: SAS. Identify the congruence theorem or postulate: Geometry Week 14 sec. 7.1 sec. 7.3 section 7.1 Triangle congruence can be proved by: SAS ASA SSS SAA Identify the congruence theorem or postulate: SAS ASA SAA SAA SSS or SAS SSA* (*There is no SSA theorem.)

More information

Centroid: The point of intersection of the three medians of a triangle. Centroid

Centroid: The point of intersection of the three medians of a triangle. Centroid Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:

More information

Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade

Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources

More information

Name: Chapter 4 Guided Notes: Congruent Triangles. Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester

Name: Chapter 4 Guided Notes: Congruent Triangles. Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester Name: Chapter 4 Guided Notes: Congruent Triangles Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester CH. 4 Guided Notes, page 2 4.1 Apply Triangle Sum Properties triangle polygon

More information

Final Review Geometry A Fall Semester

Final Review Geometry A Fall Semester Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over

More information

Geometry Essential Curriculum

Geometry Essential Curriculum Geometry Essential Curriculum Unit I: Fundamental Concepts and Patterns in Geometry Goal: The student will demonstrate the ability to use the fundamental concepts of geometry including the definitions

More information

CONJECTURES - Discovering Geometry. Chapter 2

CONJECTURES - Discovering Geometry. Chapter 2 CONJECTURES - Discovering Geometry Chapter C-1 Linear Pair Conjecture - If two angles form a linear pair, then the measures of the angles add up to 180. C- Vertical Angles Conjecture - If two angles are

More information

GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!

GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA- (x₂-x₁)²+(y₂-y₁)² Find the distance between the points ( -3,2) and

More information

1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?

1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above? 1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width

More information

ABC is the triangle with vertices at points A, B and C

ABC is the triangle with vertices at points A, B and C Euclidean Geometry Review This is a brief review of Plane Euclidean Geometry - symbols, definitions, and theorems. Part I: The following are symbols commonly used in geometry: AB is the segment from the

More information

Unit 3: Triangle Bisectors and Quadrilaterals

Unit 3: Triangle Bisectors and Quadrilaterals Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties

More information

Chapter 6 Notes: Circles

Chapter 6 Notes: Circles Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment

More information

56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.

56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points. 6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which

More information

Topics Covered on Geometry Placement Exam

Topics Covered on Geometry Placement Exam Topics Covered on Geometry Placement Exam - Use segments and congruence - Use midpoint and distance formulas - Measure and classify angles - Describe angle pair relationships - Use parallel lines and transversals

More information

Chapters 6 and 7 Notes: Circles, Locus and Concurrence

Chapters 6 and 7 Notes: Circles, Locus and Concurrence Chapters 6 and 7 Notes: Circles, Locus and Concurrence IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of

More information

Geometry: Euclidean. Through a given external point there is at most one line parallel to a

Geometry: Euclidean. Through a given external point there is at most one line parallel to a Geometry: Euclidean MATH 3120, Spring 2016 The proofs of theorems below can be proven using the SMSG postulates and the neutral geometry theorems provided in the previous section. In the SMSG axiom list,

More information

Semester Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

Semester Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question. Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Are O, N, and P collinear? If so, name the line on which they lie. O N M P a. No,

More information

Chapter 5: Relationships within Triangles

Chapter 5: Relationships within Triangles Name: Chapter 5: Relationships within Triangles Guided Notes Geometry Fall Semester CH. 5 Guided Notes, page 2 5.1 Midsegment Theorem and Coordinate Proof Term Definition Example midsegment of a triangle

More information

Geometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment

Geometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points

More information

Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1

Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the

More information

**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle.

**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Geometry Week 7 Sec 4.2 to 4.5 section 4.2 **The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Protractor Postulate:

More information

Geometry Chapter 5 Relationships Within Triangles

Geometry Chapter 5 Relationships Within Triangles Objectives: Section 5.1 Section 5.2 Section 5.3 Section 5.4 Section 5.5 To use properties of midsegments to solve problems. To use properties of perpendicular bisectors and angle bisectors. To identify

More information

Geometry Unit 1. Basics of Geometry

Geometry Unit 1. Basics of Geometry Geometry Unit 1 Basics of Geometry Using inductive reasoning - Looking for patterns and making conjectures is part of a process called inductive reasoning Conjecture- an unproven statement that is based

More information

Incenter Circumcenter

Incenter Circumcenter TRIANGLE: Centers: Incenter Incenter is the center of the inscribed circle (incircle) of the triangle, it is the point of intersection of the angle bisectors of the triangle. The radius of incircle is

More information

Geometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures.

Geometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures. Geometry: Unit 1 Vocabulary 1.1 Undefined terms Cannot be defined by using other figures. Point A specific location. It has no dimension and is represented by a dot. Line Plane A connected straight path.

More information

A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. Perpendicular Bisector Theorem

A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. Perpendicular Bisector Theorem Perpendicular Bisector Theorem A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. Converse of the Perpendicular Bisector Theorem If a

More information

Unit 1: Similarity, Congruence, and Proofs

Unit 1: Similarity, Congruence, and Proofs Unit 1: Similarity, Congruence, and Proofs This unit introduces the concepts of similarity and congruence. The definition of similarity is explored through dilation transformations. The concept of scale

More information

Congruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key

Congruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key Instruction Goal: To provide opportunities for students to develop concepts and skills related to identifying and constructing angle bisectors, perpendicular bisectors, medians, altitudes, incenters, circumcenters,

More information

Triangles can be classified by angles and sides. Write a good definition of each term and provide a sketch: Classify triangles by angles:

Triangles can be classified by angles and sides. Write a good definition of each term and provide a sketch: Classify triangles by angles: Chapter 4: Congruent Triangles A. 4-1 Classifying Triangles Identify and classify triangles by angles. Identify and classify triangles by sides. Triangles appear often in construction. Roofs sit atop a

More information

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle. Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.

More information

Math 3372-College Geometry

Math 3372-College Geometry Math 3372-College Geometry Yi Wang, Ph.D., Assistant Professor Department of Mathematics Fairmont State University Fairmont, West Virginia Fall, 2004 Fairmont, West Virginia Copyright 2004, Yi Wang Contents

More information

Selected practice exam solutions (part 5, item 2) (MAT 360)

Selected practice exam solutions (part 5, item 2) (MAT 360) Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On

More information

1.2 Informal Geometry

1.2 Informal Geometry 1.2 Informal Geometry Mathematical System: (xiomatic System) Undefined terms, concepts: Point, line, plane, space Straightness of a line, flatness of a plane point lies in the interior or the exterior

More information

Conjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)

Conjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true) Mathematical Sentence - a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement

More information

Coordinate Coplanar Distance Formula Midpoint Formula

Coordinate Coplanar Distance Formula Midpoint Formula G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the oneand two-dimensional coordinate systems to

More information

/27 Intro to Geometry Review

/27 Intro to Geometry Review /27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the

More information

GEOMETRY FINAL EXAM REVIEW

GEOMETRY FINAL EXAM REVIEW GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.

More information

Chapter Three. Parallel Lines and Planes

Chapter Three. Parallel Lines and Planes Chapter Three Parallel Lines and Planes Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately

More information

2.1 Use Inductive Reasoning

2.1 Use Inductive Reasoning 2.1 Use Inductive Reasoning Obj.: Describe patterns and use inductive reasoning. Key Vocabulary Conjecture - A conjecture is an unproven statement that is based on observations. Inductive reasoning - You

More information

Name Geometry Exam Review #1: Constructions and Vocab

Name Geometry Exam Review #1: Constructions and Vocab Name Geometry Exam Review #1: Constructions and Vocab Copy an angle: 1. Place your compass on A, make any arc. Label the intersections of the arc and the sides of the angle B and C. 2. Compass on A, make

More information

Picture. Right Triangle. Acute Triangle. Obtuse Triangle

Picture. Right Triangle. Acute Triangle. Obtuse Triangle Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from

More information

Picture. Right Triangle. Acute Triangle. Obtuse Triangle

Picture. Right Triangle. Acute Triangle. Obtuse Triangle Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from

More information

Geometry, Final Review Packet

Geometry, Final Review Packet Name: Geometry, Final Review Packet I. Vocabulary match each word on the left to its definition on the right. Word Letter Definition Acute angle A. Meeting at a point Angle bisector B. An angle with a

More information

Math 311 Test III, Spring 2013 (with solutions)

Math 311 Test III, Spring 2013 (with solutions) Math 311 Test III, Spring 2013 (with solutions) Dr Holmes April 25, 2013 It is extremely likely that there are mistakes in the solutions given! Please call them to my attention if you find them. This exam

More information

A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:

A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of mid-point and segment bisector M If a line intersects another line segment

More information

acute angle adjacent angles angle bisector between axiom Vocabulary Flash Cards Chapter 1 (p. 39) Chapter 1 (p. 48) Chapter 1 (p.38) Chapter 1 (p.

acute angle adjacent angles angle bisector between axiom Vocabulary Flash Cards Chapter 1 (p. 39) Chapter 1 (p. 48) Chapter 1 (p.38) Chapter 1 (p. Vocabulary Flash ards acute angle adjacent angles hapter 1 (p. 39) hapter 1 (p. 48) angle angle bisector hapter 1 (p.38) hapter 1 (p. 42) axiom between hapter 1 (p. 12) hapter 1 (p. 14) collinear points

More information

5.1 Midsegment Theorem and Coordinate Proof

5.1 Midsegment Theorem and Coordinate Proof 5.1 Midsegment Theorem and Coordinate Proof Obj.: Use properties of midsegments and write coordinate proofs. Key Vocabulary Midsegment of a triangle - A midsegment of a triangle is a segment that connects

More information

State the assumption you would make to start an indirect proof of each statement.

State the assumption you would make to start an indirect proof of each statement. 1. State the assumption you would make to start an indirect proof of each statement. Identify the conclusion you wish to prove. The assumption is that this conclusion is false. 2. is a scalene triangle.

More information

Duplicating Segments and Angles

Duplicating Segments and Angles CONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson, you Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using patty

More information

COURSE OVERVIEW. PearsonSchool.com Copyright 2009 Pearson Education, Inc. or its affiliate(s). All rights reserved

COURSE OVERVIEW. PearsonSchool.com Copyright 2009 Pearson Education, Inc. or its affiliate(s). All rights reserved COURSE OVERVIEW The geometry course is centered on the beliefs that The ability to construct a valid argument is the basis of logical communication, in both mathematics and the real-world. There is a need

More information

Math 531, Exam 1 Information.

Math 531, Exam 1 Information. Math 531, Exam 1 Information. 9/21/11, LC 310, 9:05-9:55. Exam 1 will be based on: Sections 1A - 1F. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/531fa11/531.html)

More information

Math 330A Class Drills All content copyright October 2010 by Mark Barsamian

Math 330A Class Drills All content copyright October 2010 by Mark Barsamian Math 330A Class Drills All content copyright October 2010 by Mark Barsamian When viewing the PDF version of this document, click on a title to go to the Class Drill. Drill for Section 1.3.1: Theorems about

More information

Geometry. Kellenberg Memorial High School

Geometry. Kellenberg Memorial High School 2015-2016 Geometry Kellenberg Memorial High School Undefined Terms and Basic Definitions 1 Click here for Chapter 1 Student Notes Section 1 Undefined Terms 1.1: Undefined Terms (we accept these as true)

More information

Lesson 28: Properties of Parallelograms

Lesson 28: Properties of Parallelograms Student Outcomes Students complete proofs that incorporate properties of parallelograms. Lesson Notes Throughout this module, we have seen the theme of building new facts with the use of established ones.

More information

Solutions to Practice Problems

Solutions to Practice Problems Higher Geometry Final Exam Tues Dec 11, 5-7:30 pm Practice Problems (1) Know the following definitions, statements of theorems, properties from the notes: congruent, triangle, quadrilateral, isosceles

More information

CRLS Mathematics Department Geometry Curriculum Map/Pacing Guide. CRLS Mathematics Department Geometry Curriculum Map/Pacing Guide

CRLS Mathematics Department Geometry Curriculum Map/Pacing Guide. CRLS Mathematics Department Geometry Curriculum Map/Pacing Guide Curriculum Map/Pacing Guide page of 6 2 77.5 Unit : Tools of 5 9 Totals Always Include 2 blocks for Review & Test Activity binder, District Google How do you find length, area? 2 What are the basic tools

More information

Week 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test

Week 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan

More information

Angles that are between parallel lines, but on opposite sides of a transversal.

Angles that are between parallel lines, but on opposite sides of a transversal. GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,

More information

Middle Grades Mathematics 5 9

Middle Grades Mathematics 5 9 Middle Grades Mathematics 5 9 Section 25 1 Knowledge of mathematics through problem solving 1. Identify appropriate mathematical problems from real-world situations. 2. Apply problem-solving strategies

More information

INFORMATION FOR TEACHERS

INFORMATION FOR TEACHERS INFORMATION FOR TEACHERS The math behind DragonBox Elements - explore the elements of geometry - Includes exercises and topics for discussion General information DragonBox Elements Teaches geometry through

More information

CHAPTER 10 GEOMETRY: ANGLES, TRIANGLES, AND DISTANCE (3 WEEKS)...

CHAPTER 10 GEOMETRY: ANGLES, TRIANGLES, AND DISTANCE (3 WEEKS)... Table of Contents CHAPTER 10 GEOMETRY: ANGLES, TRIANGLES, AND DISTANCE (3 WEEKS)... 10.0 ANCHOR PROBLEM: REASONING WITH ANGLES OF A TRIANGLE AND RECTANGLES... 6 10.1 ANGLES AND TRIANGLES... 7 10.1a Class

More information

Formal Geometry S1 (#2215)

Formal Geometry S1 (#2215) Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following course: Formal Geometry S1 (#2215)

More information

Triangle. A triangle is a geometrical figure. Tri means three. So Triangle is a geometrical figure having 3 angles.

Triangle. A triangle is a geometrical figure. Tri means three. So Triangle is a geometrical figure having 3 angles. Triangle A triangle is a geometrical figure. Tri means three. So Triangle is a geometrical figure having 3 angles. A triangle is consisting of three line segments linked end to end. As the figure linked

More information

TABLE OF CONTENTS. Free resource from Commercial redistribution prohibited. Understanding Geometry Table of Contents

TABLE OF CONTENTS. Free resource from  Commercial redistribution prohibited. Understanding Geometry Table of Contents Understanding Geometry Table of Contents TABLE OF CONTENTS Why Use This Book...ii Teaching Suggestions...vi About the Author...vi Student Introduction...vii Dedication...viii Chapter 1 Fundamentals of

More information

Intermediate Math Circles October 10, 2012 Geometry I: Angles

Intermediate Math Circles October 10, 2012 Geometry I: Angles Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,

More information

The Protractor Postulate and the SAS Axiom. Chapter The Axioms of Plane Geometry

The Protractor Postulate and the SAS Axiom. Chapter The Axioms of Plane Geometry The Protractor Postulate and the SAS Axiom Chapter 3.4-3.7 The Axioms of Plane Geometry The Protractor Postulate and Angle Measure The Protractor Postulate (p51) defines the measure of an angle (denoted

More information

3. Lengths and areas associated with the circle including such questions as: (i) What happens to the circumference if the radius length is doubled?

3. Lengths and areas associated with the circle including such questions as: (i) What happens to the circumference if the radius length is doubled? 1.06 Circle Connections Plan The first two pages of this document show a suggested sequence of teaching to emphasise the connections between synthetic geometry, co-ordinate geometry (which connects algebra

More information

Geometry Chapter 5 Review Relationships Within Triangles. 1. A midsegment of a triangle is a segment that connects the of two sides.

Geometry Chapter 5 Review Relationships Within Triangles. 1. A midsegment of a triangle is a segment that connects the of two sides. Geometry Chapter 5 Review Relationships Within Triangles Name: SECTION 5.1: Midsegments of Triangles 1. A midsegment of a triangle is a segment that connects the of two sides. A midsegment is to the third

More information

Lesson 2: Circles, Chords, Diameters, and Their Relationships

Lesson 2: Circles, Chords, Diameters, and Their Relationships Circles, Chords, Diameters, and Their Relationships Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle. Lesson Notes Students are asked to construct

More information

PARALLEL LINES CHAPTER

PARALLEL LINES CHAPTER HPTR 9 HPTR TL OF ONTNTS 9-1 Proving Lines Parallel 9-2 Properties of Parallel Lines 9-3 Parallel Lines in the oordinate Plane 9-4 The Sum of the Measures of the ngles of a Triangle 9-5 Proving Triangles

More information

Overview Mathematical Practices Congruence

Overview Mathematical Practices Congruence Overview Mathematical Practices Congruence 1. Make sense of problems and persevere in Experiment with transformations in the plane. solving them. Understand congruence in terms of rigid motions. 2. Reason

More information

Transversals. 1, 3, 5, 7, 9, 11, 13, 15 are all congruent by vertical angles, corresponding angles,

Transversals. 1, 3, 5, 7, 9, 11, 13, 15 are all congruent by vertical angles, corresponding angles, Transversals In the following explanation and drawing, an example of the angles created by two parallel lines and two transversals are shown and explained: 1, 3, 5, 7, 9, 11, 13, 15 are all congruent by

More information

Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.

Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades. Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)

More information

Foundations of Geometry 1: Points, Lines, Segments, Angles

Foundations of Geometry 1: Points, Lines, Segments, Angles Chapter 3 Foundations of Geometry 1: Points, Lines, Segments, Angles 3.1 An Introduction to Proof Syllogism: The abstract form is: 1. All A is B. 2. X is A 3. X is B Example: Let s think about an example.

More information

The Four Centers of a Triangle. Points of Concurrency. Concurrency of the Medians. Let's Take a Look at the Diagram... October 25, 2010.

The Four Centers of a Triangle. Points of Concurrency. Concurrency of the Medians. Let's Take a Look at the Diagram... October 25, 2010. Points of Concurrency Concurrent lines are three or more lines that intersect at the same point. The mutual point of intersection is called the point of concurrency. Example: x M w y M is the point of

More information

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area?

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? 1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? (a) 20 ft x 19 ft (b) 21 ft x 18 ft (c) 22 ft x 17 ft 2. Which conditional

More information

alternate interior angles

alternate interior angles alternate interior angles two non-adjacent angles that lie on the opposite sides of a transversal between two lines that the transversal intersects (a description of the location of the angles); alternate

More information

Chapter 5.1 and 5.2 Triangles

Chapter 5.1 and 5.2 Triangles Chapter 5.1 and 5.2 Triangles Students will classify triangles. Students will define and use the Angle Sum Theorem. A triangle is formed when three non-collinear points are connected by segments. Each

More information

Distance, Midpoint, and Pythagorean Theorem

Distance, Midpoint, and Pythagorean Theorem Geometry, Quarter 1, Unit 1.1 Distance, Midpoint, and Pythagorean Theorem Overview Number of instructional days: 8 (1 day = 45 minutes) Content to be learned Find distance and midpoint. (2 days) Identify

More information

1.1 Identify Points, Lines, and Planes

1.1 Identify Points, Lines, and Planes 1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures. Key Vocabulary Undefined terms - These words do not have formal definitions, but there is agreement aboutwhat they mean.

More information

CK-12 Geometry Algebraic and Congruence Properties

CK-12 Geometry Algebraic and Congruence Properties CK-12 Geometry Algebraic and Congruence Properties Learning Objectives Understand basic properties of equality and congruence. Solve equations and justify each step in the solution. Use a 2-column format

More information

Name Period 10/22 11/1 10/31 11/1. Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem

Name Period 10/22 11/1 10/31 11/1. Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem Name Period 10/22 11/1 Vocabulary Terms: Acute Triangle Right Triangle Obtuse Triangle Scalene Isosceles Equilateral Equiangular Interior Angle Exterior Angle 10/22 Classify and Triangle Angle Theorems

More information

Geometry Enduring Understandings Students will understand 1. that all circles are similar.

Geometry Enduring Understandings Students will understand 1. that all circles are similar. High School - Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,

More information

4-1 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240.

4-1 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.

More information

Algebra Geometry Glossary. 90 angle

Algebra Geometry Glossary. 90 angle lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

More information

POTENTIAL REASONS: Definition of Congruence: Definition of Midpoint: Definition of Angle Bisector:

POTENTIAL REASONS: Definition of Congruence: Definition of Midpoint: Definition of Angle Bisector: Sec 1.6 CC Geometry Triangle Proofs Name: POTENTIAL REASONS: Definition of Congruence: Having the exact same size and shape and there by having the exact same measures. Definition of Midpoint: The point

More information