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

Save this PDF as:

Size: px
Start display at page:

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

## Transcription

1 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 and its negation have opposite truth values* Conjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true) Disjunction is true when either one part or both parts of the statement is true. (P is true, q is false P\/q is true) Give the original statement p q Converse is formed by interchanging the hypothesis and conclusion. q p Inverse is formed by negating the hypothesis and conclusion. ~p ~q Contrapositive is formed by negating and switching the hypothesis and conclusion. ~q ~P *The conditional and its contrapositive are logically equivalent* Biconditional conjunction of a conditional and its converse (p q) ^ (q p) P q means (p q) ^ (q p) It is true when both p and q have the same truth value. *Tautology is a compound statement that is always true. Opposite of a Tautology is a Contradiction.* Ex. P q [p^(~p\/q)] (p^q) T T T T F T F T T F F T

2 Contradiction a compound statement that is always false Law of Detachment P q (true) p (true) :. q is also true (conclusion) Law of Modus Tollens P q (true) ~q (true) :. ~p (true) OR [(p à q) ^ ~q] à ~P Law of Syllogism p q q r :. p r Law of Detachment (Modus Ponens) p q p :. q Law of Modus Tollens p q ~q :. ~p

3 Line a set of points that extend indefinitely in both directions. Plane a set of points which form a flat surface and extend indefinitely in all directions. Collinear points points that are on the same line. Coplanar points points that are on the same plane. Line segment or segment a set of two points called endpoints and all the points between them. Ray part of a line that starts at one point (called the endpoint) and extends endlessly in one direction Basic Properties/Postulates Reflexive Property a quantity is equal to itself Symmetric Property an equality may be expressed in any other order Transitive Property if quantities are equal to the same quantity, then they are equal to each other Substitution Property a quantity may be substituted for its equal in any expression Midpoint a midpoint divides a segment into 2 congruent segments How to Interpret a Diagram Partition Postulate the whole is equal to the sum of its parts Median of a triangle a segment drawn from ant vertex of a triangle to the MIDPOINT of the opposite side Altitude of a triangle a segment drawn from any vertex of the triangle perpendicular to the line containing the opposite side Circle a set of points in a plane that are a given distance from a given point in that plane Radius a segment drawn from the center of a circle to any point on the circle Can Assume 1. Straight lines and angles. 2. Collinearity of points. 3. Between-ness of points. 4. Relative position of points Can t Assume 1. Right angles 2. Congruent segments. 3. Congruent angles. 4. Relative sizes of segments and angles (not drawn to scale) ALWAYS start off with the Postulate of the Excluded Middle in an indirect Proof Distance between two points is the length of the line segment connecting two points.

4 Distance from a point to a line is the length of the perpendicular segment from the point to the line. The triangle Inequality Postulate - In a triangle, the sum of two side lengths is greater than the length of the third side. Parallelogram a quadrilateral in which both pairs of opposite sides are parallel Each diagonal of a parallelogram splits it into two congruent triangles. Properties: 1. Both pairs of opposite sides are congruent. 2. Both pairs of opposite angles are congruent. 3. Consecutive angles are supplementary. 4. Diagonals bisect each other. Proving a Quadrilateral is a parallelogram 1. Show that both pairs of opposite sides are parallel 2. Show that one pair of opposite sides are both parallel and congruent 3. Show that both pairs of opposite sides are congruent 4. Show that both pairs of opposite angles are congruent 5. Show that diagonals bisect each other 6. An angle is supplementary to both of its consecutive angles Rectangle a parallelogram in which at least one angle is a right angle. Properties 1. Equiangular 2. All the properties of a parallelogram 3. Diagonals are congruent Proving a Quadrilateral is a Rectangle 1. A parallelogram with at least one right angle 2. A parallelogram with congruent diagonals 3. Equiangular

5 Rhombus A parallelogram in which at least two consecutive sides are congruent Properties 1. Equilateral 2. All the properties of a parallelogram 3. Diagonals are perpendicular 4. Each diagonal bisects a pair of opposite angles Proving a Quadrilateral is a Rhombus 1. A parallelogram with at least two adjacent sides congruent. 2. A parallelogram whose diagonals are perpendicular 3. A parallelogram whose diagonals bisect one angle of the parallelogram 4. Equilateral Square a parallelogram that is both a rhombus and a rectangle Properties 1. Equiangular 2. All the properties of a parallelogram 3. Diagonals are congruent 4. Equilateral 5. Diagonals are perpendicular 6. Each diagonal bisects a pair of opposite angles Proving a Quadrilateral is a Square 1. A rhombus with one right angle 2. A rectangle with two congruent adjacent sides Trapezoid a quadrilateral with exactly one pair of parallel sides Isosceles trapezoid a trapezoid in which the nonparallel sides are congruent Properties 1. Lower base angles are congruent 2. Upper base angles are congruent 3. Diagonals are congruent

6 Kite a quadrilateral with two disjoint pairs of consecutive sides are congruent Properties 1. One diagonal is the perpendicular bisector of the other. 2. One of the diagonals bisects a pair of opposite angles. 3. One pair of opposite angles are congruent. Ratio a quotient of two numbers Proportion an equation stating that two or more ratios are equal Mean Proportion a proportion in which the means are equal Ex. ½ = 2/4 = 3/6 Triangle Mid-segment Theorem - A segment joining the midpoints of two sides of a triangle is parallel to the third side and its length is ½ the length of the third side. Median (mid-segment) of a trapezoid the segment joining the midpoints of the nonparallel sides of a trapezoid Similar polygons (~Polygons) polygons in which 1. All pairs of corresponding angles are congruent 2. The ratios of the lengths of all pairs of corresponding sides are equal Proving triangles similar if there exists a correspondence between the vertices of two triangles such that (AA~ Theorem) Two angles of one triangle are congruent to the corresponding angles of the other then the triangles are similar. (SSS~ Theorem) the ratio of the measures of the corresponding sides are equal then the triangles are similar. (SAS~ Theorem) the ratios of the measures of two pairs of corresponding sides are equal and the included angles are congruent, then the triangles are similar. Side Splitter Theorem (Triangle Proportionality Theorem) if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally Theorem if an altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the given right triangle and to each other

7 Leg 1 Altitude Leg 2 Segment 1 Segment 2 Segment 1 = Altitude Altitude Segment 2 Hypotenuse = Leg 1 Leg 1 Segment 1 Altitude Rule The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Leg Rule Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg of the hypotenuse. Angle Side Measures 30 o 60 o 90 o 45 o 45 o 90 o 60 o 45 o 2x X x x 2 90 o 30 o x 3 90 o 45 o x

8 Areas Area of an Equilateral Triangle = (Side) 2 3/4 S Area of a Rhombus = d 1 d 2 /2 d 2 d 1 Scale factor = Ratio of Similitude s 1 /s 2 = P 1 /P 2 (s stands for Side, P stands for Perimeter) Area of a Square = (Side) 2 Area of a Rectangle = (Base)(Height) OR (Length)(Width) Area of a Triangle = ½(Base)(Height) Area of a Trapezoid = ½ (Base 1+Base 2)(Height) OR (Median)(Height) Area of a N-gon = ½ (Apothem)(Perimeter) Median Of a Trapezoid = (Base1+Base2)/2 Radius of a regular polygon is a segment joining the center to any vertex Apothem of a regular polygon is a segment joining the center to the midpoint of any side Lines Distance Formula Distance = (Δx) 2 +(Δy) 2 Midpoint Formula M AB = (x A +X B /2),(Y A +Y B /2) The midpoint is the Average of the two points you re finding the midpoint for. Slope is the rate of change in y-value for each unit of change in x-value. Parallel lines have equal slopes. Perpendicular lines have slopes whose product is -1. (Their slopes are negative reciprocals of each other.)

9 Of parallel lines share a point, they are non-distinct. Ways to Write a Line Eqauation Point Slope Formula 1. ax+by=c 2. y-y 1 =x-x 1 (m) 3. y=mx+b Ways to Solve Linear Equations 1. Graphical Line a 2. Substitution (x,y) Line b 3x+5y=10 x-7y=12 Given equations 3x+5y=10 X=12+7y Find point of intersection of these two lines. 3(12+7y)+5y=10 x=12+7y Point of intersection: (5,-1) 36+21y+5y=10 x=12+7(-1) 26y=-26 x=5 Y=-1 3. Elimination 10x+3y=2 70x+21y=14 10x+3y=2 Point of Intersection: (-1/4,3/2) 6x-7y= x-21y=-36 10(-1/4) +3y=2 88x = -22-5/2+3y= y=9/2 X=-1/4 y=3/2

10 Quadratic Equations Quadratic equations can be written in the form y=ax 2 +bx+c Axis of Symmetry Vertical Line given by x OR x= -b/2a Vertex; min; max; turning point Vertex found by Substitution of x=-b/2a into quadratic equation. To find the y intercept, set x=0 Steps for Graphing Parabolas 1. Find Axis of Symmetry (x=-b/2a) 2. Use #1 to find Vertex. 3. Plot 2-3 points on one side of Axis of Symmetry. (y intercept is an easy one, it s simply c in y=ax 2 +bx+c) 4. Reflect each point across axis of symmetry. 5. Sketch an expanding u-shape with arrows. Circle Equation R 2 =(x-h) 2 +(y-k) 2 At a glance, you can see that (h, k) is the center of the circle. This is in Center Radius form. Completing the Square Ex. x 2 +y 2 +6x-8y-24 = 0 x 2 +6x+ +y 2-8y+ =24 To complete the square, halve the linear coefficient for x and y, then add its square to both sides of the equation. (x+3)(x+3) (y-4)(y+4) These satisfy the given equation. x 2 +6x+9+y 2-8y+16= (x+3) 2 + (y-4) 2 = 49 Center of the circle = (-3, 4) Radius = 7

11 Graphs Solve algebraically, check graphically. 3 Scenarios of Graphs 1. One intersection 2. Two intersections 3. Nothing, no slope Circular Geometry Two or more coplanar circles with the same center are called concentric circles. Two circles are congruent/ equal if they have congruent/equal radii. A point is in the interior of a circle if its distance from the center is less than the radius. A point is in the exterior of a circle if its distance from the center is larger than the radius. A point is on a circle if its distance from the center is equal to the radius. A chord of a circle is a segment joining any 2 points on the circle. A diameter of a circle is a segment (chord) that passes through the center of the circle. The distance from the center of a circle to a chord is the measure of the perpendicular segment from the center to the chord. The circumference of a circle is its perimeter. Sector of a circle is a region bounded by two radii and their intercepted arc denoted by 3 letters: center and two endpoints of the arc. Locus Locus a set of points satisfying a given equation Usual Loci a. All points equidistant from a fixed distant, d It is a circle with center d. b. All points equidistant from 2 points A&B The perpendicular bisector of line AB c. All points fixed distance d, from line l Two lines, each parallel to line l, d units to either side of line l d. All points equidistant from 2 parallel lines m & n One line parallel to m & n equidistant from each line

12 e. All points equidistant from 2 intersecting lines. Two lines bisecting angles formed by two given lines f. All points equidistant from sides of an angle. An angle bisector of that angle The perpendicular bisectors of a triangle are concurrent at a point equidistant from the vertices. This point is called the circumcenter. The angle bisectors of a triangle are concurrent at a point equidistant from the sides of the triangle. This point is the incenter. The lines containing the Altitudes of a triangle are concurrent at a point called the orthocenter. The medians of a triangle are concurrent at a point 2/3 of the way from any vertex to its opposite sides. This point is the centroid. Line Symmetry A figure has line symmetry if a line can be drawn such that each side is a mirror image of the other. Transformation change in position, size, or orientation of a figure Line Reflection - transformation that produces a mirror image of a figure on opposite side of the given line r y-axis (x, y) = (-x, y) r x-axis (x, y) = (x, -y) r y=x (x, y) = (y, x) r y=c (x, y) = (x, 2c-y) r x=c (x, y) = (2c-x, y) R o (x, y) = (-x, -y) A figure has point symmetry if it is its own image under a reflection in a point. R o, 90 (x, y) = (y, -x) R o, 180 (x, y) = (-x, -y) R o, 270 (x, y) = (y, x) R y=-x (x, y) = (-y, -x) If you can rotate your figure 180 o about the point in question, and it is still what it used to be, then it has point symmetry. T 3, -2 (x, y) = (x+3, y-2)

13 D k (x, y) = (kx, ky) Isometry a transformation that preserves distance Direct isometry is one that preserves order (orientation) Opposite isometry is one that changes order, or orientation, from clockwise to counterclockwise, or vice-versa. To reflect an equation in y=x, switch x and y then solve for y. Space Geometry Which of these determine a PLANE? 1 point No Two points No Three collinear points Three noncollinear points A line and a point not on the line Two intersecting lines Two parallel lines No Yes Yes Yes Yes Lateral Area & Total Area Lateral Area of a Cylinder = 2πrh Total Area of a Cylinder = 2πrh + 2πr 2

14 Lateral Area of a Cone = πrl Slant Height (l ) Total Area of a Cone = πrl + πr 2 Total Area of a Sphere = 4πr 2 Volume Volume of a Cylinder = πr 2 h Volume of a Prism = l w h Volume of a Cone = 1/3 πr 2 h Volume of a Regular Pyramid = 1/3 (Area of the base)(height) Volume of a Sphere = 4/3 πr 3 Altitude and Slant Height are different Altitude goes from the tip of the cone to the bottom. Sites you d want to visit. You should also check out the back of your text book, it has all the theorems/postulates. C: GOOD LUCK ON THE REGENTS!! ---Navida Rukhsha c:

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 0810ge. 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 information

### 55 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 information

### 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

### 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

### Geometry 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 information

### 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

### 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

### 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

### 10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres. 10.4 Day 1 Warm-up

10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres 10.4 Day 1 Warm-up 1. Which identifies the figure? A rectangular pyramid B rectangular prism C cube D square pyramid 3. A polyhedron

More information

### 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

### 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

### Geometry. Unit 6. Quadrilaterals. Unit 6

Geometry Quadrilaterals Properties of Polygons Formed by three or more consecutive segments. The segments form the sides of the polygon. Each side intersects two other sides at its endpoints. The intersections

More information

### 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

### 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

### 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

### 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

### Sum of the interior angles of a n-sided Polygon = (n-2) 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 n-sided Polygon = (n-2) 180 What you need to know: How to use the formula

More information

### 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

### Section 2.1 Rectangular Coordinate Systems

P a g e 1 Section 2.1 Rectangular Coordinate Systems 1. Pythagorean Theorem In a right triangle, the lengths of the sides are related by the equation where a and b are the lengths of the legs and c is

More information

### 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

### The 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 information

### 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.

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 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

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

### 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

### New York State Student Learning Objective: Regents Geometry

New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students

More information

### 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

### 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

### 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

### 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

### 39 Symmetry of Plane Figures

39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that

More information

### 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

### Area. Area Overview. Define: Area:

Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.

More information

### Circle Name: Radius: Diameter: Chord: Secant:

12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane

More information

### 2, 3 1, 3 3, 2 3, 2. 3 Exploring Geometry Construction: Copy &: Bisect Segments & Angles Measure & Classify Angles, Describe Angle Pair Relationship

Geometry Honors Semester McDougal 014-015 Day Concepts Lesson Benchmark(s) Complexity Level 1 Identify Points, Lines, & Planes 1-1 MAFS.91.G-CO.1.1 1 Use Segments & Congruence, Use Midpoint & 1-/1- MAFS.91.G-CO.1.1,

More information

### abscissa The horizontal or x-coordinate of a two-dimensional coordinate system.

NYS Mathematics Glossary* Geometry (*This glossary has been amended from the full SED ommencement Level Glossary of Mathematical Terms (available at http://www.emsc.nysed.gov/ciai/mst/math/glossary/home.html)

More information

### Unit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period

Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period 1 2 3 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test,

More information

### Special case: Square. The same formula works, but you can also use A= Side x Side or A= (Side) 2

Geometry Chapter 11/12 Review Shape: Rectangle Formula A= Base x Height Special case: Square. The same formula works, but you can also use A= Side x Side or A= (Side) 2 Height = 6 Base = 8 Area = 8 x 6

More information

### 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

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

More information

### 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.

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 information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 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 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

### Su.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)

MA.912.G.2 Geometry: Standard 2: Polygons - Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures

More information

### 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.

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 information

### 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

### The 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 information

### (a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units

1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 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, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

More information

### GCSE Maths Linear Higher Tier Grade Descriptors

GSE Maths Linear Higher Tier escriptors Fractions /* Find one quantity as a fraction of another Solve problems involving fractions dd and subtract fractions dd and subtract mixed numbers Multiply and divide

More information

### 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

### A COURSE OUTLINE FOR GEOMETRY DEVELOPED BY ANN SHANNON & ASSOCIATES FOR THE BILL & MELINDA GATES FOUNDATION

A COURSE OUTLINE FOR GEOMETRY DEVELOPED BY ANN SHANNON & ASSOCIATES FOR THE BILL & MELINDA GATES FOUNDATION JANUARY 2014 Geometry Course Outline Content Area G0 Introduction and Construction G-CO Congruence

More information

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, June 19, :15 a.m. to 12:15 p.m., only.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 19, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

### LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.

Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the

More information

### Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.

Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length

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 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the

More information

### 2006 ACTM STATE GEOMETRY EXAM

2006 TM STT GOMTRY XM In each of the following you are to choose the best (most correct) answer and mark the corresponding letter on the answer sheet provided. The figures are not necessarily drawn to

More information

### 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

### Higher Geometry Problems

Higher Geometry Problems ( Look up Eucidean Geometry on Wikipedia, and write down the English translation given of each of the first four postulates of Euclid. Rewrite each postulate as a clear statement

More information

### #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

### SOLVED 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 information

### Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

More information

### GEOMETRY COMMON CORE STANDARDS

1st Nine Weeks Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,

More information

### Geometry. Higher Mathematics Courses 69. Geometry

The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and

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. 1. Are O, N, and P collinear? If so, name the line on which they lie. O N M P a. No,

More information

### 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

### Geometry Credit Recovery

Geometry Credit Recovery COURSE DESCRIPTION: This is a comprehensive course featuring geometric terms and processes, logic, and problem solving. Topics include parallel line and planes, congruent triangles,

More information

### Algebra 1 EOC Appendix D MATHEMATICS GLOSSARY ALGEBRA 1 EOC AND GEOMETRY EOC

Algebra 1 EOC Appendix D MATHEMATICS GLOSSARY ALGEBRA 1 EOC AND GEOMETRY EOC The terms defined in this glossary pertain to the NGSSS in mathematics for EOC assessments in Algebra 1 and Geometry. Included

More information

### Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

More information

### 10.1: Areas of Parallelograms and Triangles

10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a

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 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

### 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

### Algebra 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 information

### 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

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

### /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

### Math 366 Definitions and Theorems

Math 366 Definitions and Theorems Chapter 11 In geometry, a line has no thickness, and it extends forever in two directions. It is determined by two points. Collinear points are points on the same line.

More information

### Interactive Math Glossary Terms and Definitions

Terms and Definitions Absolute Value the magnitude of a number, or the distance from 0 on a real number line Additive Property of Area the process of finding an the area of a shape by totaling the areas

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?

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 Math Standards and I Can Statements

Geometry Math Standards and I Can Statements Unit 1 Subsection A CC.9-12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions

More information

### **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

### The 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

### 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