Geometry Unit 6 Note Sheets Date Name of Lesson. 6.2 Parallelograms. 6.3 Tests for Parallelograms. 6.4 Rectangles. 6.5 Rhombi and Squares

Size: px
Start display at page:

Download "Geometry Unit 6 Note Sheets Date Name of Lesson. 6.2 Parallelograms. 6.3 Tests for Parallelograms. 6.4 Rectangles. 6.5 Rhombi and Squares"

Transcription

1 Date Name of Lesson 6.2 Parallelograms 6.3 Tests for Parallelograms 6.4 Rectangles 6.5 Rhombi and Squares 6.6 Trapezoids and Kites 1

2 Quadrilaterals Properties Property Parallelogram Rectangle Rhombus Square Quadrilateral Trapezoid Isosceles Trapezoid Both pairs of opp sides are Exactly 1 pair of opp sides are A A A A S N N N N N N N S A A N Diagonals are ^ S S A A S S S A Diagonals S A S A S A A S Kite Diagonals bisect each other Interior Angles add up to 360 degrees. Both pairs of opp sides All sides Both pairs of opp angles Exactly 1 pair of opp angles All angles All Ð Base Ð A A A A S S S S A A A A A A A A A A A A S S S N S S A A S S S S A A A A S S S S N N N N S S S A A A S A S S S S A A S A S S S S n/a n/a n/a n/a A S A n/a A Always N Never S Sometimes n/a not applicable 2

3 6.2 Parallelograms Notes Parallelogram Properties of Parallelograms 4

4 Find the value of each variable in the parallelogram

5 7. Determine the coordinates of the intersection of the diagonals of parallelogram FGHJ with vertices!( 2, 4), ((3, 5), +(2, 3), and,( 3, 4). Steps: 1. Name the diagonals. 2. Find the midpoint of the diagonals. 8. Determine the coordinates of the intersection of the diagonals of parallelogram RSTU with vertices -( 8, 2), /( 6, 7), 2(6, 7), and 3(4, 2). Steps: 1. Name the diagonals. 2. Find the midpoint of the diagonals. 9. 6

6 6.3 Tests for Parallelograms Notes Conditions for Parallelograms Determine whether the quadrilateral is a parallelogram. Justify your answer

7 5. If!4 = 36 1, 4( = ,,4 = 68 2, and 4+ = , find 6 and 8 so that the quadrilateral is a parallelogram. 6. Find 6 and 8 so that the quadrilateral is a parallelogram. Graph each quadrilateral with the given vertices. Determine whether the figure is a parallelogram. Justify your answer , 3, : 8, 4, ;(7, 2), and <(1, 3) Steps: 1. Find the distance of each side. 2. Find the slopes of sides. 8

8 8. =( 1, 3), -(3, 1), /(2, 3), and 2( 2, 1) Steps: 1. Find the midpoint of the diagonals. 2. Find the slopes of sides. 9. A student is given the following information and then asked to write a paragraph proof. Determine which statement would correctly complete the student s proof. Given: Parallelogram >-/2 and Parallelogram >=?3 Prove:? / Proof: We are given Parallelogram >-/2 and Parallelogram >=?3. Since opposite angles of a parallelogram are congruent, >? and > /.. A. Therefore,? / by the Transitive Property of Congruence. B. Therefore,? / by the Transformative Property of Congruence. C. Therefore,? / by the Reflective Property of Congruence. D. Therefore,? / by the Reflexive Property of Congruence. 9

9 6.4 Rectangles Notes Rectangle Properties of Rectangles Diagonals of a Rectangle A rectangular park has two walking paths as shown. 1. If >/ = 180 DEFEGH and >- = 200 DEFEGH, find =2. 2. If D >-/ = 64, find D /=-. 3. Using the rectangular park, if 2/ = 120 DEFEGH find >-. 10

10 4. Quadrilateral,4:; is a rectangle. If D 4,: = and D,:4 = , find Quadrilateral -/23 is a rectangle. If D -23 = and D /3- = 36 2, find Quadrilateral >=-/ has verticies >( 5, 3), =(1, 1), -( 1, 4), and /( 7, 0). Determine whether >=-/ is a rectangle. Find the area. Steps: 1. Find the distance of each side. 2. Find the distance of the diagonals. 3. Find the area. 11

11 7. Quadrilateral,4:; has verticies,( 2, 3), 4(1, 4), :(3, 2), and ;(0, 3). Determine whether,4:; is a rectangle. Steps: 1. Find the slopes. 8. What is the value of x in the rectangle? 9. What is the value of x in the rectangle? 12

12 6.5 Rhombi and Squares Notes Rhombus Square Diagonals of a Rhombus The diagonals of rhombus!(+, intersect at 4. Use the given information to find the each measure or value. 1. If D!,+ = 82, find D 4+,. 2. If (+ = and,+ = 56 2, find 6. The diagonals of rhombus KLMN intersect at?. Use the given information to find the each measure or value. 3. If D KNL = 39.5, find D NML. 4. If KL = 86 5 and KN = , find 6. 13

13 5.,4:; is a rhombus. If D,;: = 84 and D,4; = ( ), find the value of 6. 6.,4:; is a rhombus. If D,;: = 100 and D,4; = ( ), find the value of 6. 14

14 Conditions for Rhombi and Squares 5. Determine whether parallelogram JKLM with vertices,( 7, 2), 4(0, 4), :(9, 2), and ;(2, 4) is a rhombus, a rectangle, or a square. List all that apply. Explain (Remember to find distances, slopes, midpoints to help explain.) 6. Determine whether parallelogram ABCD with vertices P( 2, 1), Q( 1, 3), R(3, 2), and S(2, 2) is a rhombus, a rectangle, or a square. List all that apply. Explain 15

15 6.6 Trapezoids and Kites Notes Trapezoid Isosceles Trapezoid Isosceles Trapezoids The speaker shown is an isosceles trapezoid. If D!,+ = 85,!4 = 8 TUVhEH, and,( = 19 TUVhEH, find each measure. 1. D!( Each side of the basket shown is an isosceles trapezoid. If D,;: = 130, 4< = 6.7 XEEF, and ;< = 3.6 XEEF, find each measure. 3. D ;,4 4.,: 16

16 5. Quadrilateral ABCD has vertices P( 3, 4), Q(2, 5), R(3, 3), and S( 1, 0). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. 6. Quadrilateral ABCD has vertices P(5, 1), Q( 3, 1), R( 2, 3), and S(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. 17

17 midsegment of a trapezoid Trapezoid Midsegment Theorem 7. In the figure :+ is the midsegment of trapezoid!(,4. What is the value of x? 8. In the figure ;< is the midsegment of trapezoid!(,4. What is the value of x? 18

18 Kite Kites 9. If!(+, is a kite, find D (!,. 10. If KLMN is a kite, find NM. 11. If KLMN is a kite, find D LMN. 12. If ;<>= is a kite, find <>. 19

Geometry/Trigonometry Unit 5: Polygon Notes Period:

Geometry/Trigonometry Unit 5: Polygon Notes Period: Geometry/Trigonometry Unit 5: Polygon Notes Name: Date: Period: # (1) Page 270 271 #8 14 Even, #15 20, #27-32 (2) Page 276 1 10, #11 25 Odd (3) Page 276 277 #12 30 Even (4) Page 283 #1-14 All (5) Page

More information

Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets

Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of the way along each median

More information

Name: Date: Period: Lab: Inscribed Quadrilaterals

Name: Date: Period: Lab: Inscribed Quadrilaterals Name: Date: Period: Materials: ompass Straightedge Lab: Inscribed Quadrilaterals Part A: Below are different categories of quadrilaterals. Each category has 2-4 figures. Using a compass and straightedge,

More information

Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means

Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means : Analytic Proofs of Theorems Previously Proved by Synthetic Means Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of

More information

Unit 9: Quadrilaterals

Unit 9: Quadrilaterals Unit 9: Quadrilaterals Topic/Assignment I CAN statement Turned in? Properties of Quadrilaterals HW: Worksheet Properties of all Quadrilaterals Properties of Parallelograms HW: Properties of Parallelograms

More information

Honors Geometry. Worksheet 4.1: Quadrilaterals. Quadrilateral:. (definition) Parallelogram:. (definition)

Honors Geometry. Worksheet 4.1: Quadrilaterals. Quadrilateral:. (definition) Parallelogram:. (definition) Honors Geometry Name: Worksheet 4.1: Quadrilaterals Fill in the blanks using definitions and theorems about quadrilaterals. Quadrilateral:. The midquad of a quadrilateral is a. The sum of the measures

More information

Definition: Convex polygon A convex polygon is a polygon in which the measure of each interior angle is less than 180º.

Definition: Convex polygon A convex polygon is a polygon in which the measure of each interior angle is less than 180º. Definition: Convex polygon A convex polygon is a polygon in which the measure of each interior angle is less than 180º. Definition: Convex polygon A convex polygon is a polygon in which the measure of

More information

Lesson 4.3 Ways of Proving that Quadrilaterals are Parallelograms

Lesson 4.3 Ways of Proving that Quadrilaterals are Parallelograms Lesson 4.3 Ways of Proving that Quadrilaterals are Parallelograms Getting Ready: How will you know whether or not a figure is a parallelogram? By definition, a quadrilateral is a parallelogram if it has

More information

Geometry. Kites Families of Quadrilaterals Coordinate Proofs Proofs. Click on a topic to

Geometry. Kites Families of Quadrilaterals Coordinate Proofs Proofs. Click on a topic to Geometry Angles of Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Constructing Parallelograms Rhombi, Rectangles and Squares Kites Families of Quadrilaterals Coordinate

More information

Pre-AICE 2: Unit 5 Exam - Study Guide

Pre-AICE 2: Unit 5 Exam - Study Guide Pre-AICE 2: Unit 5 Exam - Study Guide 1 Find the value of x. (The figure may not be drawn to scale.) A. 74 B. 108 C. 49 D. 51 2 Find the measure of an interior angle and an exterior angle of a regular

More information

Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review

Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review Polygon a closed plane figure with at least 3 sides that are segments -the sides do not intersect except at the vertices N-gon -

More information

Polygon Interior Angles

Polygon Interior Angles Polygons can be named by the number of sides. A regular polygon has All other polygons are irregular. A concave polygon has All other polygons are convex, with all vertices facing outwards. Name each polygon

More information

GEOMETRY COORDINATE GEOMETRY Proofs

GEOMETRY COORDINATE GEOMETRY Proofs GEOMETRY COORDINATE GEOMETRY Proofs Name Period 1 Coordinate Proof Help Page Formulas Slope: Distance: To show segments are congruent: Use the distance formula to find the length of the sides and show

More information

Polygons are named by the number of sides they have:

Polygons are named by the number of sides they have: Unit 5 Lesson 1 Polygons and Angle Measures I. What is a polygon? (Page 322) A polygon is a figure that meets the following conditions: It is formed by or more segments called, such that no two sides with

More information

14. How many sides does a regular polygon have, if the measure of an interior angle is 60?

14. How many sides does a regular polygon have, if the measure of an interior angle is 60? State whether the figure is a polygon; if it is a polygon, state whether the polygon is convex or concave. HINT: No curves, no gaps, and no overlaps! 1. 2. 3. 4. Find the indicated measures of the polygon.

More information

Unit 5: Polygons and Quadrilaterals

Unit 5: Polygons and Quadrilaterals Unit 5: Polygons and Quadrilaterals Scale for Unit 5 4 Through independent work beyond what was taught in class, students could (examples include, but are not limited to): - Research a unique building

More information

SOL 6.13 Quadrilaterals

SOL 6.13 Quadrilaterals SOL 6.13 Quadrilaterals 6.13 The student will describe and identify properties of quadrilaterals. Understanding the Standard: A quadrilateral is a closed planar (two-dimensional) figure with four sides

More information

Chapter 6: Quadrilaterals. of a polygon is a segment that connects any two nonconsecutive. Triangle Quadrilateral Pentagon Hexagon

Chapter 6: Quadrilaterals. of a polygon is a segment that connects any two nonconsecutive. Triangle Quadrilateral Pentagon Hexagon Lesson 6-1: Angles of Polygons A vertices. Example: Date: of a polygon is a segment that connects any two nonconsecutive Triangle Quadrilateral Pentagon Hexagon Since the sum of the angle measures of a

More information

Unit 2 Study Guide Topics: Transformations (Activity 9) o Translations o Rotations o Reflections. o Combinations of Transformations

Unit 2 Study Guide Topics: Transformations (Activity 9) o Translations o Rotations o Reflections. o Combinations of Transformations Geometry Name Unit 2 Study Guide Topics: Transformations (Activity 9) o Translations o Rotations o Reflections You are allowed a 3 o Combinations of Transformations inch by 5 inch Congruent Polygons (Activities

More information

8 sides 17 sides. x = 72

8 sides 17 sides. x = 72 GEOMETRY Chapter 7 Review Quadrilaterals Name: Hour: Date: SECTION 1: State whether each polygon is equilateral, equiangular, or regular. 1) 2) 3) equilateral regular equiangular SECTION 2: Calculate the

More information

6.1: Date: Geometry. Polygon Number of Triangles Sum of Interior Angles

6.1: Date: Geometry. Polygon Number of Triangles Sum of Interior Angles 6.1: Date: Geometry Polygon Number of Triangles Sum of Interior Angles Triangle: # of sides: # of triangles: Quadrilateral: # of sides: # of triangles: Pentagon: # of sides: # of triangles: Hexagon: #

More information

8.1 Find Angle Measures in Polygons

8.1 Find Angle Measures in Polygons VOCABULARY 8.1 Find Angle Measures in Polygons DIAGONAL Review: EQUILATERAL EQUIANGULAR REGULAR CLASSIFYING POLYGONS Polygon Interior Angle Theorem: The sum of the measures of the interior angles of a

More information

Geo, Chap 6 Practice Test, EV Ver 1

Geo, Chap 6 Practice Test, EV Ver 1 Name: Class: _ Date: _ Geo, Chap 6 Practice Test, EV Ver 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. (6-1) Which statement is true? a. All rectangles

More information

22. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

22. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Chapter 4 Quadrilaterals 4.1 Properties of a Parallelogram Definitions 22. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. 23. An altitude of a parallelogram is the

More information

Regents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2 Page 1 Name:

Regents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2 Page 1  Name: Regents Exam Questions G.G.69: Quadrilaterals in the Coordinate Plane 2 Page 1 G.G.69: Quadrilaterals in the Coordinate Plane: Investigate, justify, and apply the properties of quadrilaterals in the coordinate

More information

6-1 Study Guide and Intervention Angles of Polygons

6-1 Study Guide and Intervention Angles of Polygons 6-1 Study Guide and Intervention Angles of Polygons Polygon Interior Angles Sum The segments that connect the nonconsecutive vertices of a polygon are called diagonals. Drawing all of the diagonals from

More information

Geometry Review for Test 3 January 13, 2016

Geometry Review for Test 3 January 13, 2016 Homework #7 Due Thursday, 14 January Ch 7 Review, pp. 292 295 #1 53 Test #3 Thurs, 14 Jan Emphasis on Ch 7 except Midsegment Theorem, plus review Betweenness of Rays Theorem Whole is Greater than Part

More information

Any questions about the material so far? About the exercises?

Any questions about the material so far? About the exercises? Any questions about the material so far? About the exercises? Here is a question for you. In the diagram on the board, DE is parallel to AC, DB = 4, AB = 9 and BE = 8. What is the length EC? Polygons Definitions:

More information

Angles of Polygons Concept Summary

Angles of Polygons Concept Summary Vocabulary and oncept heck diagonal (p. 404) isosceles trapezoid (p. 439) kite (p. 438) median (p. 440) parallelogram (p. 411) rectangle (p. 424) rhombus (p. 431) square (p. 432) trapezoid (p. 439) complete

More information

5.5 Properties of Parallelogram

5.5 Properties of Parallelogram GEOMETRY Q2T6 5.5 Exam View WS Name: Class: Date: 5.5 Properties of Parallelogram True/False Indicate whether the statement is true or false. 1. In a parallelogram, the consecutive angles are congruent.

More information

6-6 Trapezoids and Kites. Find each measure. 1. ANSWER: WT, if ZX = 20 and TY = 15 ANSWER: 5

6-6 Trapezoids and Kites. Find each measure. 1. ANSWER: WT, if ZX = 20 and TY = 15 ANSWER: 5 Find each measure 1 ANALYZE RELATIONSHIPS If ABCD is a kite, find each measure 6 AB 101 2 WT, if ZX = 20 and TY = 15 5 7 5 COORDINATE GEOMETRY Quadrilateral ABCD has vertices A ( 4, 1), B( 2, 3), C(3,

More information

Examples: Identify the following as equilateral, equiangular or regular. Using Variables: S = 180(n 2)

Examples: Identify the following as equilateral, equiangular or regular. Using Variables: S = 180(n 2) Ch. 6 Notes 6.1: Polygon Angle-Sum Theorems Examples: Identify the following as equilateral, equiangular or regular. 1) 2) 3) S = 180(n 2) Using Variables: and Examples: Find the sum of the interior angles

More information

U4 Polygon Notes January 11, 2017 Unit 4: Polygons

U4 Polygon Notes January 11, 2017 Unit 4: Polygons Unit 4: Polygons 180 Complimentary Opposite exterior Practice Makes Perfect! Example: Example: Practice Makes Perfect! Def: Midsegment of a triangle - a segment that connects the midpoints of two sides

More information

6.1 What is a Polygon?

6.1 What is a Polygon? 6. What is a Polygon? Unit 6 Polygons and Quadrilaterals Regular polygon - Polygon Names: # sides Name 3 4 raw hexagon RPTOE 5 6 7 8 9 0 Name the vertices: Name the sides: Name the diagonals containing

More information

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Four sided polygon 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Foldable The fold crease 2. Now, divide the right hand section

More information

Geometry Module 3 Unit 2 Practice Exam

Geometry Module 3 Unit 2 Practice Exam Name: Class: Date: Geometry Module 3 Unit 2 Practice Exam Short Answer 1. If BCDE is congruent to OPQR, then BC is congruent to?. 2. NPM? 3. Given QRS TUV, QS 4v 3, and TV 8v 9, find the length of QS and

More information

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. ANSWER: 32

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. ANSWER: 32 ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 4. GAMES The checkerboard below is made up of 64 congruent black and red squares. Use this information to prove that the board itself

More information

Secondary Math II Honors. Unit 4 Notes. Polygons. Name: Per:

Secondary Math II Honors. Unit 4 Notes. Polygons. Name: Per: Secondary Math II Honors Unit 4 Notes Polygons Name: Per: Day 1: Interior and Exterior Angles of a Polygon Unit 4 Notes / Secondary 2 Honors Vocabulary: Polygon: Regular Polygon: Example(s): Discover the

More information

theorems & postulates & stuff (mr. ko)

theorems & postulates & stuff (mr. ko) theorems & postulates & stuff (mr. ko) postulates 1 ruler postulate The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of

More information

A closed plane figure with at least 3 sides The sides intersect only at their endpoints. Polygon ABCDEF

A closed plane figure with at least 3 sides The sides intersect only at their endpoints. Polygon ABCDEF A closed plane figure with at least 3 sides The sides intersect only at their endpoints B C A D F E Polygon ABCDEF The diagonals of a polygon are the segments that connects one vertex of a polygon to another

More information

Geometry Unit 5 - Notes Polygons

Geometry Unit 5 - Notes Polygons Geometry Unit 5 - Notes Polygons Syllabus Objective: 5.1 - The student will differentiate among polygons by their attributes. Review terms: 1) segment 2) vertex 3) collinear 4) intersect Polygon- a plane

More information

Chapter 6 Practice Test

Chapter 6 Practice Test Find the sum of the measures of the interior angles of each convex polygon. 1. hexagon A hexagon has six sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures.

More information

Midpoint Quadrilaterals

Midpoint Quadrilaterals Math Objectives Students will explore the parallelogram formed by the midpoints of any quadrilateral. Students will further explore special outer and inner quadrilaterals formed by the connected midpoints.

More information

Name Date Class. 6. In JKLM, what is the value of m K? A 15 B 57 A RS QT C QR ST

Name Date Class. 6. In JKLM, what is the value of m K? A 15 B 57 A RS QT C QR ST Name Date Class CHAPTER 6 Chapter Review #1 Form B Circle the best answer. 1. Which best describes the figure? 6. In JKLM, what is the value of m K? A regular convex heptagon B irregular convex heptagon

More information

Classifying Quadrilaterals

Classifying Quadrilaterals Classifying Quadrilaterals 1 Special Quadrilaterals: Parallelogram A B Properties: A quadrilateral with both pairs of opposite sides parallel. Opposites sides are congruent. Opposite angles are congruent.

More information

Name of Lecturer: Mr. J.Agius. Lesson 46. Chapter 9: Angles and Shapes

Name of Lecturer: Mr. J.Agius. Lesson 46. Chapter 9: Angles and Shapes Lesson 46 Chapter 9: Angles and Shapes Quadrilaterals A quadrilateral is any four-sided shape. Any quadrilateral can be split up into two triangles by drawing in a diagonal, like this: The sum of the four

More information

Geometry. Quadrilaterals. Slide 1 / 189. Slide 2 / 189. Slide 3 / 189. Table of Contents. New Jersey Center for Teaching and Learning

Geometry. Quadrilaterals. Slide 1 / 189. Slide 2 / 189. Slide 3 / 189. Table of Contents. New Jersey Center for Teaching and Learning New Jersey enter for Teaching and Learning Slide 1 / 189 Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students

More information

6-3 Conditions for Parallelograms

6-3 Conditions for Parallelograms 6-3 Conditions for Parallelograms Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Justify each statement. 1. 2. Reflex Prop. of Conv. of Alt. Int. s Thm. Evaluate each expression for x = 12 and

More information

Student Name: Teacher: Date: Miami-Dade County Public Schools. Test: 9_12 Mathematics Geometry Exam 2

Student Name: Teacher: Date: Miami-Dade County Public Schools. Test: 9_12 Mathematics Geometry Exam 2 Student Name: Teacher: Date: District: Miami-Dade County Public Schools Test: 9_12 Mathematics Geometry Exam 2 Description: GEO Topic 5: Quadrilaterals and Coordinate Geometry Form: 201 1. If the quadrilateral

More information

Problems #1. A convex pentagon has interior angles with measures (5x 12), (2x + 100), (4x + 16), (6x + 15), and (3x + 41). Find x.

Problems #1. A convex pentagon has interior angles with measures (5x 12), (2x + 100), (4x + 16), (6x + 15), and (3x + 41). Find x. 1 Pre-AP Geometry Chapter 10 Test Review Standards/Goals: G.CO.11/ C.1.i.: I can use properties of special quadrilaterals in a proof. D.2.g.: I can identify and classify quadrilaterals, including parallelograms,

More information

Assumption High School. Bell Work. Academic institution promoting High expectations resulting in Successful students

Assumption High School. Bell Work. Academic institution promoting High expectations resulting in Successful students Bell Work Geometry 2016 2017 Day 36 Topic: Chapter 4 Congruent Figures Chapter 6 Polygons & Quads Chapter 4 Big Ideas Visualization Visualization can help you connect properties of real objects with two-dimensional

More information

0811ge. Geometry Regents Exam

0811ge. Geometry Regents Exam 0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 9 8 3 6 2 In the diagram below,. 4 Pentagon PQRST has parallel to. After a translation of, which line

More information

H Geo Final Review Packet Multiple Choice Identify the choice that best completes the statement or answers the question.

H Geo Final Review Packet Multiple Choice Identify the choice that best completes the statement or answers the question. H Geo Final Review Packet Multiple Choice Identif the choice that best completes the statement or answers the question. 1. Which angle measures approximatel 7?.. In the figure below, what is the name of

More information

4.0 independently go beyond the classroom to design a real-world connection with polygons that represents a situation in its context.

4.0 independently go beyond the classroom to design a real-world connection with polygons that represents a situation in its context. ANDERSON Lesson plans!!! Intro to Polygons 10.17.16 to 11.4.16 Level SCALE Intro to Polygons Evidence 4.0 independently go beyond the classroom to design a real-world connection with polygons that represents

More information

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 10: Proving Theorems About Parallelograms Instruction

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 10: Proving Theorems About Parallelograms Instruction Prerequisite Skills This lesson requires the use of the following skills: applying angle relationships in parallel lines intersected by a transversal applying triangle congruence postulates applying triangle

More information

Unit 6 Polygons and Quadrilaterals

Unit 6 Polygons and Quadrilaterals 6.1 What is a Polygon? A closed plane figure formed by segments that intersect only at their endpoints Regular Polygon- a polygon that is both equiangular and equilateral Unit 6 Polygons and Quadrilaterals

More information

CC Geometry H Do Now: Complete the following: Quadrilaterals

CC Geometry H Do Now: Complete the following: Quadrilaterals im #26: What are the properties of parallelograms? Geometry H o Now: omplete the following: Quadrilaterals Kite iagonals are perpendicular One pair of opposite angles is congruent Two distinct pairs of

More information

Geometry Chapter 5 Review Sheet

Geometry Chapter 5 Review Sheet Geometry hapter 5 Review Sheet Name: 1. List the 6 properties of the parallelogram. 2. List the 5 ways to prove that a quadrilateral is a parallelogram. 3. Name two properties of the rectangle that are

More information

Geometry Chapter 8 Test Review

Geometry Chapter 8 Test Review Geometry Chapter 8 Test Review Short Answer 1. Find the sum of the measures of the interior angles of the indicated convex polygon. Decagon 2. Find the sum of the measures of the interior angles of the

More information

Proving Theorems about Lines and Angles

Proving Theorems about Lines and Angles Proving Theorems about Lines and Angles Angle Vocabulary Complementary- two angles whose sum is 90 degrees. Supplementary- two angles whose sum is 180 degrees. Congruent angles- two or more angles with

More information

Spiral Back: Evaluate the following when x = -2 and y = 3 1) -4y x + (3+ x 2 ) Solve the following equations: 2) x 6 = -20 3) 2x 2 = -16 4)

Spiral Back: Evaluate the following when x = -2 and y = 3 1) -4y x + (3+ x 2 ) Solve the following equations: 2) x 6 = -20 3) 2x 2 = -16 4) Name: Date: / / Spiral Back: Evaluate the following when x = -2 and y = 3 1) -4y x + (3+ x 2 ) Let s see what you remember! Sticker Challenge! Solve the following equations: 2) x 6 = -20 3) 2x 2 = -16

More information

CHAPTER 6. SECTION 6-1 Angles of Polygons POLYGON INTERIOR ANGLE SUM

CHAPTER 6. SECTION 6-1 Angles of Polygons POLYGON INTERIOR ANGLE SUM HPTER 6 Quadrilaterals SETION 6-1 ngles of Polygons POLYGON INTERIOR NGLE SUM iagonal - a line segment that connects two nonconsecutive vertices. Polygon interior angle sum theorem (6.1) - The sum of the

More information

Conditions for Parallelograms

Conditions for Parallelograms Warm Up Justify each statement. 1. 2. Reflex Prop. of Conv. of Alt. Int. s Thm. Evaluate each expression for x = 12 and y = 8.5. 3. 2x + 7 4. 16x 9 31 183 5. (8y + 5) 73 Essential Question Unit 2D Day

More information

Unit 10 Properties of Parallelograms

Unit 10 Properties of Parallelograms Unit 10 Properties of Parallelograms Target 10.1: Use properties of parallelograms to solve problems 10.1a: Use Properties of Parallelograms 10.1b: Show that a Quadrilateral is a Parallelogram Target 10.2:

More information

Chapter 8. Quadrilaterals

Chapter 8. Quadrilaterals Chapter 8 Quadrilaterals 8.1 Find Angle Measures in Polygons Objective: Find angle measures in polygons. Essential Question: How do you find a missing angle measure in a convex polygon? 1) Any convex polygon.

More information

Geometry ~ Unit 4

Geometry ~ Unit 4 Title Quadrilaterals and Coordinate Proof CISD Safety Net Standards: G.5A Big Ideas/Enduring Understandings Module 9 Properties of quadrilaterals can be used to solve real-world problems. Suggested Time

More information

Geometry Third Quarter Study Guide

Geometry Third Quarter Study Guide Geometry Third Quarter Study Guide 1. Write the if-then form, the converse, the inverse and the contrapositive for the given statement: All right angles are congruent. 2. Find the measures of angles A,

More information

6.6 trapezoids and kites 2016 ink.notebook. January 29, Page 30 Page Kites and Trapezoids. Trapezoid Examples and Practice.

6.6 trapezoids and kites 2016 ink.notebook. January 29, Page 30 Page Kites and Trapezoids. Trapezoid Examples and Practice. 6.6 trapezoids and kites 2016 ink.notebook January 29, 2018 Page 30 Page 29 6.6 Kites and Trapezoids Page 31 Page 32 Trapezoid Examples and Practice Page 33 1 Lesson Objectives Standards Lesson Notes Lesson

More information

COORDINATE PROOFS Name Per: Date Warm- up/review. 3. What is the distance between (1, 3) and (5, 12)?

COORDINATE PROOFS Name Per: Date Warm- up/review. 3. What is the distance between (1, 3) and (5, 12)? COORDINATE PROOFS Name Per: Date Warm- up/review Distance formula: d = ( x x ) + ( y y ) 2 2 2 1 2 1 Midpoint Formula: ( x1+ x2) ( y1+ y2), 2 2 Slope Formula y y m = x x 2 1 2 1 Equation of a line: Slope

More information

Unit 3: Triangles and Polygons

Unit 3: Triangles and Polygons Unit 3: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about triangles. Objective: By the end of class, I should Example 1: Trapezoid on the coordinate plane below has the following

More information

CP1 Math 2 Cumulative Exam Review

CP1 Math 2 Cumulative Exam Review Name February 9-10, 2016 If you already printed the online copy of this document, there are answer corrections on pages 4 and 8 (shaded). Deductive Geometry (Ch. 6) Writing geometric proofs Triangle congruence

More information

6.5 Trapezoids and Kites

6.5 Trapezoids and Kites www.ck12.org Chapter 6. Polygons and Quadrilaterals 6.5 Trapezoids and Kites Learning Objectives Define and find the properties of trapezoids, isosceles trapezoids, and kites. Discover the properties of

More information

Unit Goals Stage 1. Number of Days: 14 days 1/29/18-2/16/18

Unit Goals Stage 1. Number of Days: 14 days 1/29/18-2/16/18 Number of : 14 1/29/18-2/16/18 Unit Goals Stage 1 Unit Description: Drawing on our knowledge of the definitions of special quadrilaterals and a few of their properties, students will now prove those properties

More information

Chapter Test A For use after Chapter 8

Chapter Test A For use after Chapter 8 Chapter Test A For use after Chapter Find the sum of the measures of the interior angles of the indicated convex polgon. Decagon 2. Heptagon 1-gon 30-gon The sum of the measures of the interior angles

More information

Area of triangle? Area of square? Area of Rectangle? distance formula: slope point form: slope intercept form: February 22, 2017

Area of triangle? Area of square? Area of Rectangle? distance formula: slope point form: slope intercept form: February 22, 2017 Formula Page for this Unit! Quiz tomorrow! Slope Formula: rise run slope intercept form: slope point form: distance formula: Area of triangle? Area of parallelogram? Area of square? Area of Rectangle?

More information

Review Unit 5 t Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary.

Review Unit 5 t Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary. Worksheet by Kuta oftware LLC -1- Geometry Review nit 5 t Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary. 1) 2) regular 18-gon Find

More information

ALGEBRA For each triangle, find x and the measure of each side. 1. LMN is an isosceles triangle, with LM = LN, LM = 3x 2, LN = 2x + 1, and MN = 5x 2.

ALGEBRA For each triangle, find x and the measure of each side. 1. LMN is an isosceles triangle, with LM = LN, LM = 3x 2, LN = 2x + 1, and MN = 5x 2. Find each measure ALGEBRA For each triangle, find x and the measure of each side 4 1 LMN is an isosceles triangle, with LM = LN, LM = 3x 2, LN = 2x + 1, and MN = 5x 2 a x = 1; LM = 1, LN = 3, MN = 4 b

More information

Geometry Regents Lomac Date 3/2 due 3/4 Coordinate Plane: the power of right triangles

Geometry Regents Lomac Date 3/2 due 3/4 Coordinate Plane: the power of right triangles Geometry Regents Lomac 2015-2016 Date 3/2 due 3/4 Coordinate Plane: the power of right triangles 1 Name Per LO: I can find slopes and distances for pairs of points and use them to identify congruent segments

More information

Properties of Quadrilaterals

Properties of Quadrilaterals Properties of Quadrilaterals The prefix quad means four. A quadrilateral has 4 sides, and a quad bike has 4 wheels. Quad bikes are all-terrain vehicles used by farmers and ranchers. People also race quad

More information

Quadrilaterals. Polygons Basics

Quadrilaterals. Polygons Basics Name: Quadrilaterals Polygons Basics Date: Objectives: SWBAT identify, name and describe polygons. SWBAT use the sum of the measures of the interior angles of a quadrilateral. A. The basics on POLYGONS

More information

m 6 + m 3 = 180⁰ m 1 m 4 m 2 m 5 = 180⁰ m 6 m 2 1. In the figure below, p q. Which of the statements is NOT true?

m 6 + m 3 = 180⁰ m 1 m 4 m 2 m 5 = 180⁰ m 6 m 2 1. In the figure below, p q. Which of the statements is NOT true? 1. In the figure below, p q. Which of the statements is NOT true? m 1 m 4 m 6 m 2 m 6 + m 3 = 180⁰ m 2 m 5 = 180⁰ 2. Look at parallelogram ABCD below. How could you prove that ABCD is a rhombus? Show that

More information

Unit 6: Quadrilaterals

Unit 6: Quadrilaterals Name: Geometry Period Unit 6: Quadrilaterals Part 1 of 2: Coordinate Geometry Proof and Properties! In this unit you must bring the following materials with you to class every day: Please note: Calculator

More information

Squares and Rectangles

Squares and Rectangles LESSON.1 Assignment Name Date Squares and Rectangles Properties of Squares and Rectangles 1. In quadrilateral VWXY, segments VX and WY bisect each other, and are perpendicular and congruent. Is this enough

More information

Parallelograms. MA 341 Topics in Geometry Lecture 05

Parallelograms. MA 341 Topics in Geometry Lecture 05 Parallelograms MA 341 Topics in Geometry Lecture 05 Definitions A quadrilateral is a polygon with 4 distinct sides and four vertices. Is there a more precise definition? P 1 P 2 P 3 09-Sept-2011 MA 341

More information

Transformations and Congruence

Transformations and Congruence Name Date Class UNIT 1 Transformations and Congruence Unit Test: C 1. Draw ST. Construct a segment bisector and label the intersection of segments Y. If SY = a + b, what is ST? Explain your reasoning.

More information

Introduction : Applying Lines of Symmetry

Introduction : Applying Lines of Symmetry Introduction A line of symmetry,, is a line separating a figure into two halves that are mirror images. Line symmetry exists for a figure if for every point P on one side of the line, there is a corresponding

More information

Videos, Constructions, Definitions, Postulates, Theorems, and Properties

Videos, Constructions, Definitions, Postulates, Theorems, and Properties Videos, Constructions, Definitions, Postulates, Theorems, and Properties Videos Proof Overview: http://tinyurl.com/riehlproof Modules 9 and 10: http://tinyurl.com/riehlproof2 Module 9 Review: http://tinyurl.com/module9livelesson-recording

More information

ACP GEOMETRY MIDTERM REVIEW 17/18

ACP GEOMETRY MIDTERM REVIEW 17/18 ACP GEOMETRY MIDTERM REVIEW 17/18 Chapter 1 Tools of Geometry 1. The distance between the two points is. 2. Identify what each of the following means: a) AB b) AB c) AB d) AB 3. Use the figure to answer

More information

MATH 113 Section 8.2: Two-Dimensional Figures

MATH 113 Section 8.2: Two-Dimensional Figures MATH 113 Section 8.2: Two-Dimensional Figures Prof. Jonathan Duncan Walla Walla University Winter Quarter, 2008 Outline 1 Classifying Two-Dimensional Shapes 2 Polygons Triangles Quadrilaterals 3 Other

More information

5. Trapezoid: Exactly one pair of parallel sides. 6. Isosceles Trapezoid is a trapezoid where the non-parallel sides are equal.

5. Trapezoid: Exactly one pair of parallel sides. 6. Isosceles Trapezoid is a trapezoid where the non-parallel sides are equal. Quadrilaterals page #1 Five common types of quadrilaterals are defined below: Mark each picture: 1. Parallelogram: oth pairs of opposite sides parallel. 2. Rectangle: Four right angles. 3. Rhombus: Four

More information

More About Quadrilaterals

More About Quadrilaterals More About Quadrilaterals A 4-gon Conclusion Lesson 16-1 Proving a Quadrilateral Is a Parallelogram Learning Targets: Develop criteria for showing that a quadrilateral is a parallelogram. Prove that a

More information

Unit 2: Triangles and Quadrilaterals Lesson 2.1 Apply Triangle Sum Properties Lesson 4.1 from textbook

Unit 2: Triangles and Quadrilaterals Lesson 2.1 Apply Triangle Sum Properties Lesson 4.1 from textbook Unit 2: Triangles and Quadrilaterals Lesson 2.1 pply Triangle Sum Properties Lesson 4.1 from textbook Objectives Classify angles by their sides as equilateral, isosceles, or scalene. Classify triangles

More information

EQUATIONS OF ALTITUDES, MEDIANS, and PERPENDICULAR BISECTORS

EQUATIONS OF ALTITUDES, MEDIANS, and PERPENDICULAR BISECTORS EQUATIONS OF ALTITUDES, MEDIANS, and PERPENDICULAR BISECTORS Steps to Find the Median of a Triangle: -Find the midpoint of a segment using the midpoint formula. -Use the vertex and midpoint to find the

More information

9.2 Conditions for Parallelograms

9.2 Conditions for Parallelograms Name lass ate 9.2 onditions for Parallelograms Essential Question: What criteria can you use to prove that a quadrilateral is a parallelogram? Explore G.6.E Prove a quadrilateral is a parallelogram...

More information

Polygon. Note: Each segment is called a side. Each endpoint is called a vertex.

Polygon. Note: Each segment is called a side. Each endpoint is called a vertex. Polygons Polygon A closed plane figure formed by 3 or more segments. Each segment intersects exactly 2 other segments at their endpoints. No 2 segments with a common endpoint are collinear. Note: Each

More information

Example 1: MATH is a parallelogram. Find the values of w, x, y, and z. Write an equation for each and write the property of parallelograms used.

Example 1: MATH is a parallelogram. Find the values of w, x, y, and z. Write an equation for each and write the property of parallelograms used. Name: Date: Period: Geometr Notes Parallelograms Fab Five Quadrilateral Parallelogram Diagonal Five Fabulous Facts about Parallelograms: ) ) 3) 4) 5) ***This is the Parallelogram Definition and Theorems!

More information

Geometry. Slide 1 / 343. Slide 2 / 343. Slide 3 / 343. Quadrilaterals. Table of Contents

Geometry. Slide 1 / 343. Slide 2 / 343. Slide 3 / 343. Quadrilaterals. Table of Contents Slide 1 / 343 Slide 2 / 343 Geometry Quadrilaterals 2015-10-27 www.njctl.org Table of ontents Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Rhombi, Rectangles and Squares

More information

Polygons & Quadrilaterals Classwork

Polygons & Quadrilaterals Classwork Name: Class: Date: ID: A Polygons & Quadrilaterals Classwork Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The pentagon in the diagram below is formed

More information

Use throughout the course: for example, Parallel and Perpendicular Lines Proving Lines Parallel. Polygons and Parallelograms Parallelograms

Use throughout the course: for example, Parallel and Perpendicular Lines Proving Lines Parallel. Polygons and Parallelograms Parallelograms Geometry Correlated to the Texas Essential Knowledge and Skills TEKS Units Lessons G.1 Mathematical Process Standards The student uses mathematical processes to acquire and demonstrate mathematical understanding.

More information

Unit 7: Quadrilaterals

Unit 7: Quadrilaterals Name: Geometry Period Unit 7: Quadrilaterals Part 1 of 2: Coordinate Geometry Proof and Properties! In this unit you must bring the following materials with you to class every day: Please note: Calculator

More information