Copyright 2014 Edmentum  All rights reserved. 04/01/2014 Cheryl Shelton 10 th Grade Geometry Theorems Given: Prove: Proof: Statements Reasons


 Dorthy Mathews
 2 years ago
 Views:
Transcription
1 Study Island Copyright 2014 Edmentum  All rights reserved. Generation Date: 04/01/2014 Generated By: Cheryl Shelton Title: 10 th Grade Geometry Theorems 1. Given: g h Prove: 1 and 2 are supplementary 1. g h 1. Given m 1 = m 3 3. Definition of congruent angles 4. 2 and 3 are supplementary 5. m 3 + m 2 = m 1 + m 2 = Linear Pair Postulate 5. Definition of supplementary angles 6. Substitution property of equality
2 7. 1 and 2 are supplementary 7. Definition of supplementary angles A. Alternate Exterior Angles Theorem B. Alternate Interior Angles Theorem C. Definition of congruent angles D. Definition of linear pair 2. Proving the alternate exterior angle theorem. Given: f g and line d is a transversal. Prove: Line f is parallel to line g. Line d is a transversal given If parallel lines are cut by a transversal, then corresponding angles are congruent transitive property of congruence Which of the following statements and reasons completes the proof? A. 1 4 since vertical angles are congruent. B. 5 4 since alternate interior angles are congruent. C. 5 8 since vertical angles are congruent. D. 4 8 since corresponding angles are congruent.
3 3. In the triangle below, m F = 28, m FHG = 70, and m E = 82. Determine the missing reason to prove HG DE. m F = 28, m FHG = 70, m E = 82 given m F + m FHG + m HGF = m HGF = 180 substitution sum of the interior angles of a triangle equal 180 m HGF = 82 property of subtraction m HGF = m E transitive property of equality HG DE A. B. C. D. If two corresponding angles are congruent, then the third angle is opposite a set of parallel lines. If two triangles have one or more sets of congruent angles, then the lines containing the bases are parallel. If three angles of one triangle are congruent to three angles of another triangle, then the two triangles are congruent and the bases are parallel. If two lines are cut by a transversal to form congruent corresponding angles, then the two lines are parallel.
4 4. Given: Line f is tangent to circle C at point D, 1 2 Prove: CD f 1. Line f is tangent to circle C at point D, and 2 are a linear pair 1. Given 2. Definition of linear pair 3. 1 and 2 are supplementary 3. Linear Pair Postulate 4. m 1 + m 2 = m 1 = m 2 6. m 1 + m 1 = (m 1) = m 1 = is a right angle 4. Definition of supplementary angles 5. Definition of congruent angles 6. Substitution property of equality 7. Distributive property of equality 8. Division property of equality 9. Definition of right angle
5 10. CD f 10. A. Definition of perpendicular lines and segments B. Definition of vertical angles C. Definition of parallel lines and segments D. Definition of congruent angles 5. Given: 2 and 3 are a linear pair, 3 and 4 are a linear pair Prove: and 3 are a linear pair, 3 and 4 are a linear pair 2. 2 and 3 are supplementary, 3 and 4 are supplementary Given Congruent Supplements Theorem A. Transitive Property B. Congruent Complements Theorem
6 C. Right Angle Congruence Theorem D. Linear Pair Postulate 6. Proving the sameside interior angle theorem. Given: f g and line d is a transversal. Prove: m 3 + m 5 = Line f is parallel to line g. Line d is a transversal. given 2. m 3 + m 1 = 180 linear pair property m 3 + m 5 = 180 substitution property Which of the following statements and reasons completes the proof? A. m 5 + m 7 = 180 since they form a linear pair. B. m 3 = m 7 since corresponding angles are congruent. C. m 1 = m 4 since vertical angles are congruent. D. m 1 = m 5 since corresponding angles are congruent. 7.
7 Given: Point F is the center of circle F Prove: 2 (m 1 + m 3) = m 1. Point F is the center of circle F 1. Given 2. FG, FJ, and FH are radii of circle F 3. Definition of radius 2. FG FJ FH 3. Definition of radius , m 1 = m 2, m 3 = m 4 6. m 5 = (m 1 + m 2) m 6 = (m 3 + m 4) 7. m 5 = (m 1 + m 1) m 6 = (m 3 + m 3) 8. m 5 = (m 1) m 6 = (m 3) 9. m 7 = (m 5 + m 6) 10. m 7 = (1802 (m 1))  (1802 (m 3)) 4. Definition of isosceles triangle 5. Definition of congruent angles Substitution property of equality 8. Distributive property of equality 9. Sum of angles about a point 10. Substitution property of equality 11. m 7 = 2 (m 1 + m 3) 11. Simplification 12. m = 2 (m 1 + m 3) 12. Definition of central angle
8 A. Definition of complementary angles B. Congruent Supplements Theorem C. Linear Pair Postulate D. Triangle Sum Theorem 8. Given isosceles trapezoid ABCD with DF CE and BAF CEB, determine the missing reason to prove AFD CEB. ABCD is an isosceles trapezoid given C D The base angles of an isosceles trapezoid are congruent. DF CE given AB DC definition of isosceles trapezoid AFD BAF BAF CEB given AFD CEB transitive property AFD CEB ASA A. alternate interior angles conjecture B. vertical angle conjecture C. corresponding angles conjecture D. alternate exterior angles conjecture 9.
9 Given: g h Prove: g h 1. Given m 2 = m 3 3. Definition of congruent angles Vertical Angles Theorem 5. m 1 = m 2 5. Definition of congruent angles 6. m 1 = m 3 6. Transitive property of equality Definition of congruent angles A. Definition of complementary angles B. Consecutive Interior Angles Theorem C. Corresponding Angles Postulate D. Definition of parallel lines 10. Given point D is on the bisector of CAB and AD is an altitude of CAB, determine the missing reason to prove CAD BAD. AD AD reflexive property AD is an altitude of CAB given AD CB definition of altitude CDA BDA perpendicular angles are congruent point D is on the bisector of CAB given
10 DAC DAB CAD BAD ASA A. definition of isosceles triangle B. definition of angle bisector C. reflexive property D. definition of an altitude 11. Given: 1 and 2 are complementary, 3 and 4 are complementary, 1 4 Prove: and 2 are complements, 3 and 4 are complements, m 1 + m 2 = 90 m 3 + m 4 = Given 2. Definition of complementary angles 3. m 1 + m 2 = m 3 + m 4 3. Transitive property of equality 4. m 1 = m m 1 + m 2 = m 3 + m 1 6. m 2 = m Substitution property of equality 6. Subtraction property of equality 7. Definition of congruent angles
11 A. Definition of congruent angles B. Transitive Property of Angle Congruence C. Definition of complementary angles D. Right Angle Congruence Theorem 12. Proving the vertical angle theorem. Given: 1 and 2 are vertical angles. Prove: and 2 are vertical angles given 2. m 1 + m 3 = 180 m 2 + m 3 = 180 linear pair property 3. m 1 + m 3 = m 2 + m 3 substitution property 4. m 1 = m 2 A. subtraction property B. reflexive property C. addition property D. transitive property 13. Given: 1 and 2 are supplementary, 2 and 3 are supplementary Prove: 1 3
12 1. 1 and 2 are supplements, 2 and 3 are supplements 2. m 1 + m 2 = 180 m 2 + m 3 = m 1 + m 2 = m 2 + m 3 4. m 1 = m Given Transitive property of equality 4. Subtraction property of equality 5. Definition of congruent angles A. Definition of supplementary angles B. Definition of complementary angles C. Transitive property of equality D. Substitution property of equality 14. Given: 1 2, 1 and 2 are a linear pair Prove: p q 1. 1 and 2 are a linear pair 1. Given 2. 1 and 2 are 2. Linear Pair Postulate
13 supplementary 3. m 1 + m 2 = Definition of supplementary angles 4. Given 5. m 1 = m 2 6. m 1 + m 1 = Definition of congruent angles 6. Substitution property of equality 7. 2 (m 1) = Distributive property 8. m 1 = Division property of equality 9. 1 is a right angle 9. Definition of a right angle 10. p q 10. A. Definition of parallel lines B. Definition of perpendicular lines C. Linear Pair Postulate D. Congruent Supplements Theorem 15. Given m M = 23 and M P, determine the missing reason to prove MNP is obtuse. m M = 23 and M P given m P = 23 transitive property of equality m M + m N + m P = m N + 23 = 180 substitution m N = 134 addition property of equality N is obtuse definition of obtuse angle
14 MNP is obtuse definition of obtuse triangle A. The square of the length of the third side of a triangle is equal to the sum of the squares of the other two sides. B. The sum of the interior angles of a triangle equals 180. C. Correpsonding angles sum to 180. D. Adjacent angles in a triangle are congruent. 16. Given: ABC with exterior 4 Prove: m 4 = m 1 + m 2 1. ABC with exterior 4 Given 2. m 4 + m 3 = 180 Linear Pair 3. m 1 + m 2 + m 3 = 180 Triangle Sum Theorem 4. Substitution Property 5. m 4 = m 1 + m 2 Subtraction Property A. m 4 + m 3 = m 1 + m 2 + m 4 B. m 4 + m 3 = m 1 + m 2 + m 3 C. m 1 + m 3 + m 4 = 180 D. m 1 + m 2 + m 4 = 180
15 17. Given m FAH = m CBD + m CDB, determine the missing statement in the proof below. m FAH = m CBD + m CDB m DCE = m CBD + m CDB m FAH = m DCE given The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. transitive property of equality converse of the alternate exterior angle conjecture A. B. m FAH = m DCB C. CBD is isosceles D. 18. Proving the congruent supplements theorem. Given: 1 3, 1 and 2 are supplementary, and 3 and 4 are supplementary. Prove: 2 4
16 1. m 1 + m 2 = 180 m 3 + m 4 = m 1 + m 2 = m 3 + m 4 definition of supplementary angles substitution property m 1 = m 3 given 4. m 1 + m 2 = m 1 + m 4 5. m 2 = m subtraction property A. addition property B. substitution property C. reflexive property D. symmetric property 19. Given: CB Prove: m BCA + m CAB + m ABC = CB Given 2. m DAC + m CAB + m BAE = 180 Angle Addition
17 3. m DAC = m BCA m BAE = m ABC m BCA + m CAB + m ABC = 180 Substitution Property Alternate Exterior Angles; A. Alternate Exterior Angles B. C. D. Alternate Exterior Angles; Alternate Interior Angles Alternate Interior Angles; Alternate Exterior Angles Alternate Interior Angles; Alternate Interior Angles 20. Given: 3 and 4 are a linear pair, 1 and 3 are supplementary Prove: g h 1. 3 and 4 are a linear pair, 1. Given
18 1 and 3 are supplementary 2. 3 and 4 are supplementary 2. Linear Pair Postulate 3. m 1 + m 3 = 180 m 3 + m 4 = m 1 + m 3 = m 3 + m 4 5. m 1 = m g h 3. Definition of supplementary angles 4. Transitive property of equality 5. Subtraction property of equality 6. Definition of congruent angles 7. A. Alternate Interior Angles Theorem B. Alternate Exterior Angles Theorem C. Linear Pair Postulate D. Corresponding Angles Postulate 21. In the triangles below, NP RP, and PM PQ. Determine the missing reason to prove that MNP QRP. Statement NP RP, PM PQ Reason given m NPM = m RPQ MNP QRP SAS
19 A. An angle is congruent to itself. B. Alternate exterior angles are congruent. C. Vertical angles are congruent. D. Alternate interior angles are congruent. 22. Proving the alternate interior angle theorem. Given: f g and line d is a transversal. Prove: Line f is parallel to line g. Line d is a transversal given If parallel lines are cut by a transversal, then corresponding angles are congruent transitive property of congruence Which of the following statements and reasons completes the proof? A. B. C. D. 1 8 since alternate exterior angles are congruent. 5 8 since vertical angles are congruent. 1 4 since vertical angles are congruent. 4 8 since corresponding angles are congruent.
20 23. In scalene triangle WXY below, WYA BAY. Determine the missing reason to prove AXB ~ WXY. WYA BAY given AB WY If two parallel lines are cut by a transversal, then alternate interior angles are congruent. XWY XYW XAB XBA X AXB ~ X WXY reflexive property If three angles of one triangle are congruent to three angles of another triangle, then the two triangles are similar. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. A. B. If two angles are congruent to the same angle, then they are congruent. C. If two parallel lines are cut by a transversal, then corresponding angles are congruent. D. If two angles are vertical angles, then they are congruent.
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 informationBlue Pelican Geometry Theorem Proofs
Blue Pelican Geometry Theorem Proofs Copyright 2013 by Charles E. Cook; Refugio, Tx (All rights reserved) Table of contents Geometry Theorem Proofs The theorems listed here are but a few of the total in
More informationIntermediate 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 information1. 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 informationDefinitions, 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 informationChapter 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 informationABC 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 informationStudent Name: Teacher: Date: District: MiamiDade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1
Student Name: Teacher: Date: District: MiamiDade 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 informationPOTENTIAL 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 informationChapter 4 Study guide
Name: Class: Date: ID: A Chapter 4 Study guide Numeric Response 1. An isosceles triangle has a perimeter of 50 in. The congruent sides measure (2x + 3) cm. The length of the third side is 4x cm. What is
More informationHow Do You Measure a Triangle? Examples
How Do You Measure a Triangle? Examples 1. A triangle is a threesided polygon. A polygon is a closed figure in a plane that is made up of segments called sides that intersect only at their endpoints,
More informationChapter 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 informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your
More information/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 informationMath 531, Exam 1 Information.
Math 531, Exam 1 Information. 9/21/11, LC 310, 9:059:55. 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 informationA 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 midpoint and segment bisector M If a line intersects another line segment
More informationQuadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid
Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,
More information55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points.
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
More informationGEOMETRY 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 informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More informationName: 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 informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationOn Geometric Proofs: Base angles of an isosceles trapezoid are equal Perpendicular bisectors of a triangle meet at a common point
On Geometric Proofs: Base angles of an isosceles trapezoid are equal Perpendicular bisectors of a triangle meet at a common point Before demonstrating the above proofs, we should review what sort of geometric
More informationGEOMETRY 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 (x₂x₁)²+(y₂y₁)² Find the distance between the points ( 3,2) and
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationAlgebraic Properties and Proofs
Algebraic Properties and Proofs Name You have solved algebraic equations for a couple years now, but now it is time to justify the steps you have practiced and now take without thinking and acting without
More informationDEFINITIONS. 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 informationMath 3372College Geometry
Math 3372College 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 informationGeometry 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 information1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.
Quadrilaterals  Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals  Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,
More informationTopics 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 informationMathematics 3301001 Spring 2015 Dr. Alexandra Shlapentokh Guide #3
Mathematics 3301001 Spring 2015 Dr. Alexandra Shlapentokh Guide #3 The problems in bold are the problems for Test #3. As before, you are allowed to use statements above and all postulates in the proofs
More informationConjectures 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 informationAlgebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
More informationQuadrilaterals. Definition
Quadrilaterals Definition A quadrilateral is a foursided closed figure in a plane that meets the following conditions: Each side has its endpoints in common with an endpoint of two adjacent sides. Consecutive
More informationCHAPTER 8 QUADRILATERALS. 8.1 Introduction
CHAPTER 8 QUADRILATERALS 8.1 Introduction You have studied many properties of a triangle in Chapters 6 and 7 and you know that on joining three noncollinear points in pairs, the figure so obtained is
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationTriangles. Triangle. a. What are other names for triangle ABC?
Triangles Triangle A triangle is a closed figure in a plane consisting of three segments called sides. Any two sides intersect in exactly one point called a vertex. A triangle is named using the capital
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, January 26, 2016 1:15 to 4:15 p.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, January 26, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The possession or use of any communications
More informationChapter 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 information3.1 Triangles, Congruence Relations, SAS Hypothesis
Chapter 3 Foundations of Geometry 2 3.1 Triangles, Congruence Relations, SAS Hypothesis Definition 3.1 A triangle is the union of three segments ( called its side), whose end points (called its vertices)
More informationSolutions to Practice Problems
Higher Geometry Final Exam Tues Dec 11, 57:30 pm Practice Problems (1) Know the following definitions, statements of theorems, properties from the notes: congruent, triangle, quadrilateral, isosceles
More informationGeometry EOC Practice Test #2
Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply
More informationChapters 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 informationGeometry 1. Unit 3: Perpendicular and Parallel Lines
Geometry 1 Unit 3: Perpendicular and Parallel Lines Geometry 1 Unit 3 3.1 Lines and Angles Lines and Angles Parallel Lines Parallel lines are lines that are coplanar and do not intersect. Some examples
More information0810ge. Geometry Regents Exam 0810
0810ge 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More informationSolutions to inclass problems
Solutions to inclass problems College Geometry Spring 2016 Theorem 3.1.7. If l and m are two distinct, nonparallel lines, then there exists exactly one point P such that P lies on both l and m. Proof.
More informationSemester 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 informationCurriculum Map by Block Geometry Mapping for Math Block Testing 20072008. August 20 to August 24 Review concepts from previous grades.
Curriculum Map by Geometry Mapping for Math Testing 20072008 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 informationSOLVED PROBLEMS REVIEW COORDINATE GEOMETRY. 2.1 Use the slopes, distances, line equations to verify your guesses
CHAPTER SOLVED PROBLEMS REVIEW COORDINATE GEOMETRY For the review sessions, I will try to post some of the solved homework since I find that at this age both taking notes and proofs are still a burgeoning
More informationGeometry in a Nutshell
Geometry in a Nutshell Henry Liu, 26 November 2007 This short handout is a list of some of the very basic ideas and results in pure geometry. Draw your own diagrams with a pencil, ruler and compass where
More informationLesson 18: Looking More Carefully at Parallel Lines
Student Outcomes Students learn to construct a line parallel to a given line through a point not on that line using a rotation by 180. They learn how to prove the alternate interior angles theorem using
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationMost popular response to
Class #33 Most popular response to What did the students want to prove? The angle bisectors of a square meet at a point. A square is a convex quadrilateral in which all sides are congruent and all angles
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More informationA. 3y = 2x + 1. y = x + 3. y = x  3. D. 2y = 3x + 3
Name: Geometry Regents Prep Spring 2010 Assignment 1. Which is an equation of the line that passes through the point (1, 4) and has a slope of 3? A. y = 3x + 4 B. y = x + 4 C. y = 3x  1 D. y = 3x + 1
More information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what
More informationProof Case #1 CD AE. AE is the altitude to BC. Given: CD is the altitude to AB. Prove: ABC is isosceles
Proof Case #1 B Given: CD is the altitude to AB AE is the altitude to BC CD AE Prove: ABC is isosceles D E A C Proof Case # 2 Given: AB CD DC bisects ADE Prove: ABD is isosceles Proof Case #3 Given: 1
More informationUnit 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 informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 20, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More informationSession 5 Dissections and Proof
Key Terms for This Session Session 5 Dissections and Proof Previously Introduced midline parallelogram quadrilateral rectangle sideangleside (SAS) congruence square trapezoid vertex New in This Session
More informationChapter 4.1 Parallel Lines and Planes
Chapter 4.1 Parallel Lines and Planes Expand on our definition of parallel lines Introduce the idea of parallel planes. What do we recall about parallel lines? In geometry, we have to be concerned about
More informationGeometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
More informationTerminology: When one line intersects each of two given lines, we call that line a transversal.
Feb 23 Notes: Definition: Two lines l and m are parallel if they lie in the same plane and do not intersect. Terminology: When one line intersects each of two given lines, we call that line a transversal.
More informationGeometry 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 informationGEOMETRY: TRIANGLES COMMON MISTAKES
GEOMETRY: TRIANGLES COMMON MISTAKES 1 GeometryClassifying Triangles How Triangles are Classified TypesTriangles are classified by Angles or Sides By Angles Obtuse Trianglestriangles with one obtuse
More informationFind the measure of each numbered angle, and name the theorems that justify your work.
Find the measure of each numbered angle, and name the theorems that justify your work. 1. The angles 2 and 3 are complementary, or adjacent angles that form a right angle. So, m 2 + m 3 = 90. Substitute.
More informationChapter 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 noncollinear points are connected by segments. Each
More informationFinal 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 informationCHAPTER 7 TRIANGLES. 7.1 Introduction. 7.2 Congruence of Triangles
CHAPTER 7 TRIANGLES 7.1 Introduction You have studied about triangles and their various properties in your earlier classes. You know that a closed figure formed by three intersecting lines is called a
More information1 Solution of Homework
Math 3181 Dr. Franz Rothe February 4, 2011 Name: 1 Solution of Homework 10 Problem 1.1 (Common tangents of two circles). How many common tangents do two circles have. Informally draw all different cases,
More informationDetermining Angle Measure with Parallel Lines Examples
Determining Angle Measure with Parallel Lines Examples 1. Using the figure at the right, review with students the following angles: corresponding, alternate interior, alternate exterior and consecutive
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationSum of the interior angles of a nsided Polygon = (n2) 180
5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a nsided Polygon = (n2) 180 What you need to know: How to use the formula
More informationGeometry CP Lesson 51: Bisectors, Medians and Altitudes Page 1 of 3
Geometry CP Lesson 51: Bisectors, Medians and Altitudes Page 1 of 3 Main ideas: Identify and use perpendicular bisectors and angle bisectors in triangles. Standard: 12.0 A perpendicular bisector of a
More informationVocabulary. Term Page Definition Clarifying Example. biconditional statement. conclusion. conditional statement. conjecture.
CHAPTER Vocabulary The table contains important vocabulary terms from Chapter. As you work through the chapter, fill in the page number, definition, and a clarifying example. biconditional statement conclusion
More informationGeo, Chap 4 Practice Test, EV Ver 1
Class: Date: Geo, Chap 4 Practice Test, EV Ver 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. (43) In each pair of triangles, parts are congruent as
More informationLesson 10.1 Skills Practice
Lesson 0. Skills Practice Name_Date Location, Location, Location! Line Relationships Vocabulary Write the term or terms from the box that best complete each statement. intersecting lines perpendicular
More informationIsosceles triangles. Key Words: Isosceles triangle, midpoint, median, angle bisectors, perpendicular bisectors
Isosceles triangles Lesson Summary: Students will investigate the properties of isosceles triangles. Angle bisectors, perpendicular bisectors, midpoints, and medians are also examined in this lesson. A
More informationGeometryUnit 3 Study Guide
Name: Class: Date: GeometryUnit 3 Study Guide Determine the slope of the line that contains the given points. Refer to the figure below. 1 TÊ Á 6, 3 ˆ, V Ê Á 8, 8 ˆ A 2 5 B 5 2 C 0 D 2 5 Solve the system
More informationCircle Theorems. This circle shown is described an OT. As always, when we introduce a new topic we have to define the things we wish to talk about.
Circle s circle is a set of points in a plane that are a given distance from a given point, called the center. The center is often used to name the circle. T This circle shown is described an OT. s always,
More information116 Chapter 6 Transformations and the Coordinate Plane
116 Chapter 6 Transformations and the Coordinate Plane Chapter 61 The Coordinates of a Point in a Plane Section Quiz [20 points] PART I Answer all questions in this part. Each correct answer will receive
More informationUse the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. 1. measures less than By the Exterior Angle Inequality Theorem, the exterior angle ( ) is larger than
More informationFoundations 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 informationQUADRILATERALS CHAPTER 8. (A) Main Concepts and Results
CHAPTER 8 QUADRILATERALS (A) Main Concepts and Results Sides, Angles and diagonals of a quadrilateral; Different types of quadrilaterals: Trapezium, parallelogram, rectangle, rhombus and square. Sum of
More informationLesson 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 informationGeometry: 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 informationQuadrilaterals Unit Review
Name: Class: Date: Quadrilaterals Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) In which polygon does the sum of the measures of
More informationSelected 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 informationEuclidean Geometry. We start with the idea of an axiomatic system. An axiomatic system has four parts:
Euclidean Geometry Students are often so challenged by the details of Euclidean geometry that they miss the rich structure of the subject. We give an overview of a piece of this structure below. We start
More information3.1. Angle Pairs. What s Your Angle? Angle Pairs. ACTIVITY 3.1 Investigative. Activity Focus Measuring angles Angle pairs
SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Use Manipulatives Two rays with a common endpoint form an angle. The common endpoint is called the vertex. You can use a protractor to draw and measure
More informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More informationName 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 informationGeometry: 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 informationhttp://jsuniltutorial.weebly.com/ Page 1
Parallelogram solved Worksheet/ Questions Paper 1.Q. Name each of the following parallelograms. (i) The diagonals are equal and the adjacent sides are unequal. (ii) The diagonals are equal and the adjacent
More informationAngles 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 information2.1. Inductive Reasoning EXAMPLE A
CONDENSED LESSON 2.1 Inductive Reasoning In this lesson you will Learn how inductive reasoning is used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers
More informationChapter 4: Congruent Triangles
Name: Chapter 4: Congruent Triangles Guided Notes Geometry Fall Semester 4.1 Apply Triangle Sum Properties CH. 4 Guided Notes, page 2 Term Definition Example triangle polygon sides vertices Classifying
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More information