HIGH SCHOOL. Geometry. Soowook Lee

Size: px
Start display at page:

Download "HIGH SCHOOL. Geometry. Soowook Lee"

Transcription

1 HIGH SHOOL Geometry Soowook Lee

2 hapter 4 Quadrilaterals This chapter will cover basic quadrilaterals, including parallelograms, trapezoids, rhombi, rectangles, squares, kites, and cyclic quadrilaterals.

3 Section 1 Parallelograms (properties) February 11, 2012 Parallelogram WE WILL ISUSS... quadrilateral with both pairs of opposite sides parallel. 1. efinition 2. iscovery of Properties Figure 1. Various Parallelograms parallelogram is a quadrilateral with 3. Summary 4. Related Problems opposite sides parallel. It is the "parent" of some other quadrilaterals, which are obtained by adding restrictions of various kinds Parallelogram Exercise 1. Let (-2, 3), (5, 3), (0, -1), and (a, -1) be vertices of a parallelogram on a cartesian plane. Find the value of a. Video solution to Ex. 1 2

4 Exercise 2. In parallelogram, diagonal is drawn. Prove that Triangle is congruent to Triangle. Use the definition of a parallelogram. Knowing the triangles are congruent form Ex. 2, what can you observe about corresponding parts of the triangles from the parallelogram? List all you observe. Figure 2. Parallelogram with diagonal Figure 3. Properties of a Parallelogram (part 1) Swipe to see the next step diagonal forms two congruent triangles in a parallelogram. Video solution to Ex. 2 So far, we have Opposite sides are parallel. (efinition) 2. Opposite sides are congruent. 3. Opposite angles are congruent. 4. diagonal divides the parallelogram into two congruent triangles. 3

5 Exercise 3. In parallelogram, diagonal and are drawn, intersecting at E. Using the previously discussed properties of a parallelogram, show that Triangle E is congruent to Triangle E. Reflecting on the congruent triangles from Ex. 3, what can you conclude about diagonals in parallelogram? List a couple of things you observe. Figure 4. Parallelogram with diagonals and Figure 5. Properties of Parallelogram (part 2) E E Swipe to see the next steps y congruent corresponding parts in congruent triangles, we see that diagonals are bisected. Video solution to Ex. 3 More properties, 5. iagonals bisect each other. 6. iagonals divides a parallelogram into four triangles with equal area. *(See Prob. 2) 7. onsecutive interior angles are supplementary. *(See Prob. 1) 4

6 Problems 1. Prove that consecutive interior angles in a parallelogram are supplementary. (hint: efinition of a parallelogram) 4. In the diagram below of parallelogram MTH,,, and. T What is the perimeter of the parallelogram? 2. In parallelogram, diagonals and are drawn, intersecting at E. Show that the diagonals create four triangles with equal areas. M a. 1 b. 3 c. 8 d. 16 H 3. In the diagram below of parallelogram with diagonals and,, and. What is the measure of? E Which statement is not true about every parallelogram? a. Two pairs of opposite sides are congruent. b. Two pairs of opposite angles are congruent. c. onsecutive interior angles are congruent. d. The diagonals bisect each other. a. 15 o b. 20 o c. 25 o d. 70 o 5

7 6. In parallelogram JETS, JE =10 and ET = 8. What is a possible length of diagonal JT? a. 2 b. 12 c. 18 d Parallelogram QWER has coordinates Q (2, 2), W (-1, 6), E (1, 9), and R (4, 5). Prove that diagonals of QWER bisect each other. 7. In parallelogram GEOM with G (2, 0), E (8, 0), and O (6, 4),,,, and are midpoints of sides GE, EO, OM, and MG, respectively. Show that is also a parallelogram. Then, find the ratio of areas between parallelograms GEOM and. 6

8 Section 2 Parallelogram (proofs) WE WILL ISUSS How we can show that a quadrilateral is a parallelogram, using the definition and properties. 2. Methods of proving a quadrilateral is a parallelogram. 3. Related Problems How do we prove that a quadrilateral is a parallelogram? We can show this by satisfying the definition of a parallelogram. s we have discussed in the previous section, a parallelogram is a quadrilateral when two pairs of opposite sides are parallel. Exercise 1. Quadrilateral has two pairs of congruent opposite sides, that is = and =. Show that is a parallelogram. Figure 1. Quadrilateral Video solution to Ex. 1 Swipe for a hint 7

9 s we can see from the previous exercise, a property of a parallelogram can be used to prove that a quadrilateral is a parallelogram. Let us examine other properties to see if they are enough to show that a quadrilateral is a parallelogram. Exercise 2. Quadrilateral EFGH has two pairs of congruent opposite interior angles. Show that EFGH is a parallelogram. So far, we have seen that properties of a parallelogram are useful tool to show that a quadrilateral is a parallelogram. The next exercise will use another property of a parallelogram. Exercise 3. Quadrilateral IJKL has diagonals bisecting each other. Show that IJKL is a parallelogram. Figure 3. Quadrilateral with bisecting diagonals Figure 2. Quadrilateral with congruent opposite angles E F I J H G L K swipe for a hint swipe for a hint Video solution to Ex. 2 Video solution to Ex. 3 8

10 So far, we know that a quadrilateral is a parallelogram if two pairs of opposite sides are parallel. 2. two pairs of opposite sides are congruent. 3. two pairs of opposite angles are congruent. 4. two diagonals bisect each other. 5. one pair of opposite sides are congruent and parallel. (See prob. 1) 9

11 Problems 1. Show that when a quadrilateral has a pair of congruent and parallel sides, it is a parallelogram. 3. Show that why a pair of congruent opposite sides and another pair of parallel opposite sides in a quadrilateral are not sufficient enough to prove that it is a parallelogram. 2. Quadrilateral QWER has coordinates Q (2, 2), W (-1, 6), E (4, 5), and R (1, 9). Show that it is a parallelogram. 4. parallelogram has coordinates (1, 3), (-2, 6), and (0, -2). Find all possible coordinates for the last vertex. 10

12 5. Quadrilateral FOUR has coordinates F (1, 6), O (7, 4), U (-3, 0), and R (-7, 2). Show that midpoints of the quadrilateral form a parallelogram. 6. Given: Quadrilateral, diagonal FE,,,, Prove: is a parallelogram. 1 E F 2 11

13 Section 3 Rhombi (properties) WE WILL ISUSS efinition 2. iscovery of Properties 3. Summary 4. Related Problems Rhombus quadrilateral with all four sides equal in length; an equilateral quadrilateral rhombus is known as a special parallelogram. an you show why a quadrilateral with four congruent sides is a parallelogram? Exercise 1. Prove that a quadrilateral with four sides with equal length is a parallelogram. Figure 1. an equilateral quadrilateral Video Solution to Ex. 1 12

14 Since a rhombus is a parallelogram, all properties of a parallelogram are valid in a rhombus. Let s continue to discover more properties of a rhombus. Exercise 2. Rhombus has a diagonal. Using the definition of a rhombus, show that triangle and are congruent. What can you observe about the diagonals from having both triangles congruent to each other? See the diagrams below. Figure 3. Property of a rhombus Figure 2. Rhombus with a diagonal ue to congruent triangles, corresponding angles are congruent. swipe for a hint So far, we know that a rhombus has all congruent sides. (efinition) 2. is a parallelogram. Therefore, it has all the properties of a parallelogram. 3. iagonals bisect vertex angles. 13

15 Exercise 3. In rhombus JUNE, diagonals JN and UE intersect M. Show that triangle JMU is congruent to triangle NMU. Figure 4. rhombus with two diagonals U Since the consecutive triangles are congruent, what can you conclude about angle JMU and angle NMU? They are congruent and a linear pair. This implies that the given angles are right angles. Slides 1. Properties of a rhombus J M N E swipe for a hint 14

16 Problems 1. lengths of diagonals of a rhombus are 10 and 24. What is the perimeter of the rhombus? 3. Two congruent equilateral triangles with side of length of 4 units are overlapped as shown below, creating a rhombus in the middle. Vertex of each triangle is tangent to the midpoint of a side of the other triangle. What is the perimeter of the rhombus? 2. In rhombus, E = 6 and measure of angle E is 60 degrees. Find the perimeter and the area of the rhombus. E 4. In the diagram below of rhombus,. What is? 1) 40 2) 45 3) 50 4) 80 15

17 5. In rhombus, the measures in inches of is 3x + 2 and is x Find the number of inches in the length of. 7. Rhombus FEGH has coordinates of F(3, 2), E(0, 6), and G(-3, 2). Find the coordinates of H. 6. n equilateral triangle and a rhombus with an interior angle of 60 o have the perimeters of 12 inches. What is the ratio of areas between the triangle and the rhombus? 16

18 Parallel a. (of straight lines) lying in the same plane but never meeting no matter how far extended. b. (of planes) having common perpendiculars. c. (of a single line, plane, etc.) equidistant from another or others (usually followed by to or with ). Related Glossary Terms rag related terms here Index Find Term

19 Parallelogram quadrilateral with both pairs of opposite sides parallel Related Glossary Terms Quadrilateral Index Find Term

20 Quadrilateral a polygon with four sides Related Glossary Terms Parallelogram Index Find Term

HIGH SCHOOL. Geometry. Soowook Lee

HIGH SCHOOL. Geometry. Soowook Lee HIGH SCHOOL Geometry Soowook Lee Chapter 4 Quadrilaterals This chapter will cover basic quadrilaterals, including parallelograms, trapezoids, rhombi, rectangles, squares, kites, and cyclic quadrilaterals.

More information

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

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

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

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

Geometry R Quadrilateral Packet Due 1/17/17 Name. A) Diagonal bisect each other B) Opposite angles are congruent

Geometry R Quadrilateral Packet Due 1/17/17 Name. A) Diagonal bisect each other B) Opposite angles are congruent Geometry R Quadrilateral Packet ue 1/17/17 Name MULTIPLE HOIE 1. Which of the following is NOT a characteristic of all parallelograms? ) iagonal bisect each other ) Opposite angles are congruent ) iagonals

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

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

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 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

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

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

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

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

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

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

5.6notes November 13, Based on work from pages , complete In an isosceles triangle, the &

5.6notes November 13, Based on work from pages , complete In an isosceles triangle, the & chapter 5 Based on work from pages 178-179, complete In an isosceles triangle, the & & & drawn from the vertex angle of an isosceles triangle are the! 5.1 Indirect proof. G: DB AC F is the midpt. of AC

More information

pd 3notes 5.4 November 09, 2016 Based on work from pages , complete In an isosceles triangle, the &

pd 3notes 5.4 November 09, 2016 Based on work from pages , complete In an isosceles triangle, the & chapter 5 Based on work from pages 178-179, complete In an isosceles triangle, the & & & drawn from the vertex angle of an isosceles triangle are the! 5.1 Indirect proof. G: DB AC F is the midpt. of AC

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

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

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

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

Geometry Regents Lomac Date 11/20 due 11/23 Using Congruent Triangles to prove Quadrilateral Properties

Geometry Regents Lomac Date 11/20 due 11/23 Using Congruent Triangles to prove Quadrilateral Properties Geometry Regents Lomac 2015-2016 Date 11/20 due 11/23 Using Congruent Triangles to prove Quadrilateral Properties 1 Name Per LO: I can prove statements by first proving that triangles are congruent and

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

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

Sorting Quadrilaterals Activity a. Remove the Concave quadrilaterals? Which did you remove?

Sorting Quadrilaterals Activity a. Remove the Concave quadrilaterals? Which did you remove? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Sorting Quadrilaterals Activity 1a. Remove the Concave quadrilaterals? Which did you remove? 3. 6. From Geometry Teacher s Activity Workbook p 114 & 115 1b. The Rest

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

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

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

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 Vocabulary Math Fundamentals Reference Sheet Page 1

Geometry Vocabulary Math Fundamentals Reference Sheet Page 1 Math Fundamentals Reference Sheet Page 1 Acute Angle An angle whose measure is between 0 and 90 Acute Triangle A that has all acute Adjacent Alternate Interior Angle Two coplanar with a common vertex and

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

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

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

Unit 1.5: Quadrilaterals: Day 5 Quadrilaterals Review

Unit 1.5: Quadrilaterals: Day 5 Quadrilaterals Review P1 Math 2 Unit 1.5: Quadrilaterals: ay 5 Quadrilaterals Review Name t our next class meeting, we will take a quiz on quadrilaterals. It is important that you can differentiate between the definition of

More information

Parallel Lines cut by a Transversal Notes, Page 1

Parallel Lines cut by a Transversal Notes, Page 1 Angle Relationships Review 2 When two lines intersect, they form four angles with one point in 1 3 common. 4 Angles that are opposite one another are VERTIAL ANGLES. Some people say instead that VERTIAL

More information

Polygon notes

Polygon notes 1.6-6.1 Polygon notes Polygon: Examples: Nonexamples: Named by the letters of the vertices written in order polygon will be: oncave - Or: onvex- Regular Polygon: 1.6-6.1 Polygon notes iagonal is a segment

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

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

Geometry Ch 7 Quadrilaterals January 06, 2016

Geometry Ch 7 Quadrilaterals January 06, 2016 Theorem 17: Equal corresponding angles mean that lines are parallel. Corollary 1: Equal alternate interior angles mean that lines are parallel. Corollary 2: Supplementary interior angles on the same side

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

Mrs. Daniel s Geometry Vocab List

Mrs. Daniel s Geometry Vocab List Mrs. Daniel s Geometry Vocab List Geometry Definition: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Refectional Symmetry Definition:

More information

Understanding Quadrilaterals

Understanding Quadrilaterals Understanding Quadrilaterals Parallelogram: A quadrilateral with each pair of opposite sides parallel. Properties: (1) Opposite sides are equal. (2) Opposite angles are equal. (3) Diagonals bisect one

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

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name ate hapter 7 Maintaining Mathematical Proficiency Solve the equation by interpreting the expression in parentheses as a single quantity. 1. 5( 10 x) = 100 2. 6( x + 8) 12 = 48 3. ( x) ( x) 32 + 42

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

Properties of Rhombuses, Rectangles, and Squares

Properties of Rhombuses, Rectangles, and Squares 6- Properties of Rhombuses, Rectangles, and Squares ontent Standards G.O. Prove theorems about parallelograms... rectangles are parallelograms with congruent diagonals. lso G.SRT.5 Objectives To define

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

Vocabulary. Term Page Definition Clarifying Example base angle of a trapezoid. base of a trapezoid. concave (polygon) convex (polygon)

Vocabulary. Term Page Definition Clarifying Example base angle of a trapezoid. base of a trapezoid. concave (polygon) convex (polygon) HPTER 6 Vocabulary The table contains important vocabulary terms from hapter 6. s you work through the chapter, fill in the page number, definition, and a clarifying example. Term Page efinition larifying

More information

Review for Quadrilateral Test

Review for Quadrilateral Test Review for Quadrilateral Test 1. How many triangles are formed by drawing diagonals from one vertex in the figure? Find the sum of the measures of the angles in the figure. a. 6, 1080 b. 7, 1260 c. 7,

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

ACTM Geometry Exam State 2010

ACTM Geometry Exam State 2010 TM Geometry xam State 2010 In each of the following select the answer and record the selection on the answer sheet provided. Note: Pictures are not necessarily drawn to scale. 1. The measure of in the

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

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

MANHATTAN HUNTER SCIENCE HIGH SCHOOL GEOMETRY CURRICULUM

MANHATTAN HUNTER SCIENCE HIGH SCHOOL GEOMETRY CURRICULUM COORDINATE Geometry Plotting points on the coordinate plane. Using the Distance Formula: Investigate, and apply the Pythagorean Theorem as it relates to the distance formula. (G.GPE.7, 8.G.B.7, 8.G.B.8)

More information

Capter 6 Review Sheet. 1. Given the diagram, what postulate or theorem would be used to prove that AP = CP?

Capter 6 Review Sheet. 1. Given the diagram, what postulate or theorem would be used to prove that AP = CP? apter 6 Review Sheet Name: ate: 1. Given the diagram, what postulate or theorem would be used to prove that P = P? 4.. S. SSS.. SS 2. Given the diagram, what postulate or theorem would be used to prove

More information

CHAPTER 8 QUADRILATERALS

CHAPTER 8 QUADRILATERALS HTE 8 UILTEL In this chapter we address three ig IE: ) Using angle relationships in polygons. ) Using properties of parallelograms. 3) lassifying quadrilaterals by the properties. ection: Essential uestion

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

An angle that has a measure less than a right angle.

An angle that has a measure less than a right angle. Unit 1 Study Strategies: Two-Dimensional Figures Lesson Vocab Word Definition Example Formed by two rays or line segments that have the same 1 Angle endpoint. The shared endpoint is called the vertex.

More information

Math Polygons

Math Polygons Math 310 9.2 Polygons Curve & Connected Idea The idea of a curve is something you could draw on paper without lifting your pencil. The idea of connected is that a set can t be split into two disjoint sets.

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

Geometry Foundations Planning Document

Geometry Foundations Planning Document Geometry Foundations Planning Document Unit 1: Chromatic Numbers Unit Overview A variety of topics allows students to begin the year successfully, review basic fundamentals, develop cooperative learning

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

Math 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK

Math 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK Math 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK [acute angle] [acute triangle] [adjacent interior angle] [alternate exterior angles] [alternate interior angles] [altitude] [angle] [angle_addition_postulate]

More information

Geometry. (1) Complete the following:

Geometry. (1) Complete the following: (1) omplete the following: 1) The area of the triangle whose base length 10cm and height 6cm equals cm 2. 2) Two triangles which have the same base and their vertices opposite to this base on a straight

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

Class VIII Chapter 3 Understanding Quadrilaterals Maths. Exercise 3.1

Class VIII Chapter 3 Understanding Quadrilaterals Maths. Exercise 3.1 Question 1: Given here are some figures. Exercise 3.1 (1) (2) (3) (4) (5) (6) (7) (8) Classify each of them on the basis of the following. (a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex

More information

T103 Final Review Sheet. Central Angles. Inductive Proof. Transversal. Rectangle

T103 Final Review Sheet. Central Angles. Inductive Proof. Transversal. Rectangle T103 Final Review Sheet Know the following definitions and their notations: Point Hexa- Space Hepta- Line Octa- Plane Nona- Collinear Deca- Coplanar Dodeca- Intersect Icosa- Point of Intersection Interior

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

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

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

Unit 6 Review Geometry Name Date: Section: CONSTRUCTION OF A SQUARE INSCRIBED IN A CIRCLE. Key Idea: Diagonals of a square are of each other.

Unit 6 Review Geometry Name Date: Section: CONSTRUCTION OF A SQUARE INSCRIBED IN A CIRCLE. Key Idea: Diagonals of a square are of each other. Name ate: Section: ONSTRUTION OF SQURE INSRIE IN IRLE Key Idea: iagonals of a square are of each other. Steps: 1) raw a. 2) the diameter. 3) onnect the four points on the circle to make the of the square.

More information

Instructional Unit CPM Geometry Unit Content Objective Performance Indicator Performance Task State Standards Code:

Instructional Unit CPM Geometry Unit Content Objective Performance Indicator Performance Task State Standards Code: 306 Instructional Unit Area 1. Areas of Squares and The students will be -Find the amount of carpet 2.4.11 E Rectangles able to determine the needed to cover various plane 2. Areas of Parallelograms and

More information

STANDARDS OF LEARNING CONTENT REVIEW NOTES GEOMETRY. 3 rd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES GEOMETRY. 3 rd Nine Weeks, STANDARDS OF LEARNING CONTENT REVIEW NOTES GEOMETRY 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource for

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

Perimeter. Area. Surface Area. Volume. Circle (circumference) C = 2πr. Square. Rectangle. Triangle. Rectangle/Parallelogram A = bh

Perimeter. Area. Surface Area. Volume. Circle (circumference) C = 2πr. Square. Rectangle. Triangle. Rectangle/Parallelogram A = bh Perimeter Circle (circumference) C = 2πr Square P = 4s Rectangle P = 2b + 2h Area Circle A = πr Triangle A = bh Rectangle/Parallelogram A = bh Rhombus/Kite A = d d Trapezoid A = b + b h A area a apothem

More information

Geometry Final Exam - Study Guide

Geometry Final Exam - Study Guide Geometry Final Exam - Study Guide 1. Solve for x. True or False? (questions 2-5) 2. All rectangles are rhombuses. 3. If a quadrilateral is a kite, then it is a parallelogram. 4. If two parallel lines 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

EXPLORING QUADRILATERALS AND PARALLELOGRAMS

EXPLORING QUADRILATERALS AND PARALLELOGRAMS EXPLORING QUADRILATERALS AND PARALLELOGRAMS PREPARED BY MIKE NEDROW 2001 Quadrilaterals Exploring Parallelograms This Geometer s Sketchpad activity will investigate quadrilaterals and parallelograms which

More information

Unit 2: Triangles and Polygons

Unit 2: Triangles and Polygons Unit 2: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about lines and angles. Objective: By the end of class, I should Using the diagram below, answer the following questions. Line

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

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

Measurement and Geometry (M&G3)

Measurement and Geometry (M&G3) MPM1DE Measurement and Geometry (M&G3) Please do not write in this package. Record your answers to the questions on lined paper. Make notes on new definitions such as midpoint, median, midsegment and any

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

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

Int. Geometry Unit 7 Test Review 1

Int. Geometry Unit 7 Test Review 1 Int. Geometry Unit 7 est eview uestions -0: omplete each statement with sometimes, always, or never.. he diagonals of a trapezoid are congruent.. rhombus is equiangular.. rectangle is a square.. he opposite

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

November 10, 2004 : Fax:

November 10, 2004 : Fax: Honors Geometry Issue Super Mathter November 0, 004 : 30-0-6030 Fax: 30--864 For class info, visit www.mathenglish.com irect your questions and comments to rli@smart4micro.com Name: Peter Lin Peter Lin

More information

0613ge. Geometry Regents Exam 0613

0613ge. Geometry Regents Exam 0613 wwwjmaporg 0613ge 1 In trapezoid RSTV with bases and, diagonals and intersect at Q If trapezoid RSTV is not isosceles, which triangle is equal in area to? 2 In the diagram below, 3 In a park, two straight

More information

GEOMETRY is the study of points in space

GEOMETRY is the study of points in space CHAPTER 5 Logic and Geometry SECTION 5-1 Elements of Geometry GEOMETRY is the study of points in space POINT indicates a specific location and is represented by a dot and a letter R S T LINE is a set of

More information

STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks, STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource

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

Lines Plane A flat surface that has no thickness and extends forever.

Lines Plane A flat surface that has no thickness and extends forever. Lines Plane A flat surface that has no thickness and extends forever. Point an exact location Line a straight path that has no thickness and extends forever in opposite directions Ray Part of a line that

More information

Answer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers

Answer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers 1.1 The Three Dimensions 1. Possible answer: You need only one number to describe the location of a point on a line. You need two numbers to describe the location of a point on a plane. 2. vary. Possible

More information

Geometry SOL Study Sheet. 1. Slope: ! y 1 x 2. m = y 2. ! x Midpoint: + x y 2 2. midpoint = ( x 1. , y Distance: (x 2 ) 2

Geometry SOL Study Sheet. 1. Slope: ! y 1 x 2. m = y 2. ! x Midpoint: + x y 2 2. midpoint = ( x 1. , y Distance: (x 2 ) 2 Geometry SOL Study Sheet 1. Slope: 2. Midpoint: 3. Distance: m = y 2! y 1 x 2! x 1 midpoint = ( x 1 + x 2 2, y 1 + y 2 2 ) d = (x 2! x 1 ) 2 + (y 2! y 1 ) 2 4. Sum of Interior Angles (Convex Polygons):

More information

5-1 Properties of Parallelograms. Objectives Apply the definition of a. parallelogram,

5-1 Properties of Parallelograms. Objectives Apply the definition of a. parallelogram, hapter 5 Quadrilaterals 5-1 Properties of Parallelograms Quadrilaterals pply the definition of a Prove that certain quadrilaterals are s pply the theorems and definitions about the special quadrilaterals

More information

Assignment. Quilting and Tessellations Introduction to Quadrilaterals. List all of the types of quadrilaterals that have the given characteristics.

Assignment. Quilting and Tessellations Introduction to Quadrilaterals. List all of the types of quadrilaterals that have the given characteristics. Assignment Assignment for Lesson.1 Name Date Quilting and Tessellations Introduction to Quadrilaterals List all of the types of quadrilaterals that have the given characteristics. 1. four right angles

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

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