Similar Polygons. Copy both triangles onto tracing paper. Measure and record the sides of each triangle. Cut out both triangles.

Size: px
Start display at page:

Download "Similar Polygons. Copy both triangles onto tracing paper. Measure and record the sides of each triangle. Cut out both triangles."

Transcription

1 -7 Similar Polygons MAIN IDEA Identify similar polygons and find missing measures of similar polygons. New Vocabulary polygon similar corresponding parts congruent scale factor Math Online glencoe.com Etra Eamples Personal Tutor Self-Check Quiz Follow the steps below to discover how the triangles at the right are related. Copy both triangles onto tracing paper. Measure and record the sides of each triangle. Cut out both triangles. 1. Compare the angles of the triangles by matching them up. Identify the angle pairs that have equal measure.. Epress the ratios _ DF LK, _ EF JK, and _ DE as decimals to the nearest tenth. LJ. What do you notice about the ratios of these sides of matching triangles? A polygon consists of a sequence of consecutive line segments in a plane, placed end to end to form a simple closed figure. Polygons that have the same shape are called similar polygons. In the figure below, polygon ABCD is similar to polygon WXYZ. This is written as polygon ABCD polygon WXYZ. The parts of similar figures that match are called corresponding parts. Corresponding Angles A W, B X, C Y, D Z Corresponding Sides AB WX, BC XY, CD YZ, DA ZW 1 Chapter Proportions and Similarity

2 The similar triangles in the Mini Lab suggest the following. Similar Polygons Key Concept Reading Math Congruence The symbol is read is congruent to. Arcs are used to show congruent angles. Words Model Symbols If two polygons are similar, then their corresponding angles are congruent, or have the same measure, and the measures of their corresponding sides are proportional. ABC XYZ _ AB_ A X, B Y, C Z, and XY = BC AC_ YZ = XZ Identify Similar Polygons Common Error Do not assume that two polygons are similar just because their corresponding angles are congruent. Their corresponding sides must also be proportional. 1 Determine whether rectangle HJKL is similar to rectangle MNPQ. Eplain. First, check to see if corresponding angles are congruent. Since the two polygons are rectangles, all of their angles are right angles. Therefore, all corresponding angles are congruent. Net, check to see if corresponding sides are proportional. JK_ NP = _ or _ 1 _ HJ MN = _ 7 Since _ 7 and _ 1 _ KL PQ = _ LH_ QM = _ or _ 1 are not equivalent ratios, rectangle HJKL is not similar to rectangle MNPQ. Determine whether these polygons are similar. Eplain. a. b The ratio of the lengths of two corresponding sides of two similar polygons is called the scale factor. You can use the scale factor of similar figures or a proportion to find missing measures. Lesson -7 Similar Polygons 19

3 Find Missing Measures GEOMETRY Given that polygon WXYZ polygon ABCD, find the missing measure. 1 1 m Reading Math Segment Measure The measure of XY is written as XY. It represents a number. METHOD 1 Write a proportion. The missing measure m is the length of XY. Write a proportion. polygon WXYZ polygon ABCD _ XY BC = _ YZ CD m_ = _ 1 m = 1 m = polygon WXYZ polygon ABCD XY = m, BC =, YZ = 1, and CD =. Find the cross products. Multiply. m = 1 Divide each side by. Scale Factor In Eample, the scale factor from polygon ABCD to polygon WXYZ is _, which means that a length _ on polygon ABCD is as long as a length on polygon WXYZ. METHOD Use the scale factor to write an equation. Find the scale factor from polygon WXYZ to polygon ABCD. scale factor: _ YZ CD = _ 1 or _ The scale factor is the constant of proportionality. _ Words A length on is times as a corresponding length Variable Equation polygon WXYZ m = _ () Write the equation. m = 1 Multiply. Find each missing measure above. long as Let m represent the measure of XY. m = _ on polygon ABCD. c. WZ d. AB Square A square B with a scale factor of :. Notice that the ratio of their perimeters is : or :. m m Square A Perimeter m B m Square A Square B 0 Chapter Proportions and Similarity

4 This and other related eamples suggest the following. Ratios of Similar Figures Key Concept Words If two figures are a_ similar with a scale factor of, then the b perimeters of the figures have a ratio of a_ b. Model a Figure A b Figure B Similarity Statements In naming similar triangles, the order of the vertices indicates the corresponding parts. Read the similarity statement carefully to be sure that you compare corresponding parts. Triangle LMN is similar to triangle PQR. If the perimeter of LMN is units, what is the perimeter of PQR? A units B 9 units 1 C units D units Read the Item You know the measures of two corresponding sides and the perimeter of LMN. You need to find the perimeter of PQR. Solve the Item Triangle LMN triangle PQR with a scale factor of _ 1 or _. The ratio of the perimeters of LMN to PQR is also _. perimeter of LMN _ perimeter of PQR = _ Scale factor relating LMN to PQR = Find the cross products. The answer is C. 19 = Multiply. _ 19 _ = Divide each side by. = Simplify. e. Square KLMN is similar to square TUVW. If the perimeter of square KLMN is units, what is the perimeter of square TUVW? 1 F units H units G 9 units J 0 units Lesson -7 Similar Polygons 1

5 Eample 1 (p. 19) Eample (p. 0) Determine whether each pair of polygons is similar. Eplain. 1.. In the figure at the right, FGH KLJ. Write and solve a proportion to find each missing side measure y Eample (p. 1). MULTIPLE CHOICE ABC is similar to XYZ. If the perimeter of ABC is 0 units, what is the perimeter of XYZ? A units B 0 units C 0 units D 0 units 1 For Eercises 9 1, 19 HELP HOMEWORK HELP See Eamples 1 Determine whether each pair of polygons is similar. Eplain Each pair of polygons is similar. Write and solve a proportion to find each missing side measure Chapter Proportions and Similarity

6 1. LIFE SCIENCE The scale factor from the model of a human inner ear to the actual ear is :. If one of the bones of the model is. centimeters long, how long is the actual bone in a human ear? PRACTICE EXTRA PRACTICE See pages 79, TELEVISION The ratio of the length of a wide-screen TV to its width is 1:9. Find the width of a wide-screen TV if the length measures inches. Round to the nearest tenth. H.O.T. Problems 1. CHALLENGE Suppose two rectangles are similar with a scale factor of. What is the ratio of their areas? Eplain. WRITING IN MATH Determine whether each statement is always, sometimes, or never true. Eplain your reasoning. 1. Any two rectangles are similar. 17. Any two squares are similar. 1. Triangle FGH is similar to triangle RST. F in. in. G 1 in. What is the length of TS? H A 1 _ 1 inches C inches? 7 in. B _ inches D 1 _ inches T R S 19. Quadrilateral ABCD is similar to quadrilateral WXYZ. in. in. If the perimeter of quadrilateral ABCD is units, what is the perimeter of quadrilateral WXYZ? F 1. inches H 7 inches G inches J inches 0. ROCK CLIMBING Grace is working her way up a climbing wall. Every minutes she is able to climb feet, but then loses her footing, slips back 1 foot, and decides to rest for 1 minute. If the rock wall is 0 feet tall, how long will it take her to reach the top? Use the draw a diagram strategy. (Lesson -) Solve each proportion. (Lesson -) 1. _ = _ y. _ 0 b = _ 0. _ 0. = _ 1. n PREREQUISITE SKILL Graph and connect each pair of ordered pairs. (Lesson -). (-., 1.), (1., -.). (-, -1 1_, ) (, _ 1. 1_ ) (-, 1 ), (, _ ) Lesson -7 Similar Polygons

6.1 Ratios, Proportions, and the Geometric Mean

6.1 Ratios, Proportions, and the Geometric Mean 6.1 Ratios, Proportions, and the Geometric Mean Obj.: Solve problems by writing and solving proportions. Key Vocabulary Ratio - If a and b are two numbers or quantities and b 0, then the ratio of a to

More information

Original Coordinates. Graph a Dilation (10 _ 1 2, 6 _ 1 2 ) K (5, 3) 2, 2 1 _ 2 ) L (4, 1)

Original Coordinates. Graph a Dilation (10 _ 1 2, 6 _ 1 2 ) K (5, 3) 2, 2 1 _ 2 ) L (4, 1) 4-8 Dilations Main IDEA Graph dilations on a coordinate plane. New Vocabular dilation center enlargement reduction Math nline glencoe.com Concepts in Motion Etra Eamples Personal Tutor Self-Check Quiz

More information

Unit 5 - Test Study Guide

Unit 5 - Test Study Guide Class: Date: Unit 5 - Test Study Guide 1. Which of these transformations appear to be a rigid motion? (I) parallelogram EFGH parallelogram XWVU (II) hexagon CDEFGH hexagon YXWVUT (III) triangle EFG triangle

More information

How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures

How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures .6 Perimeters and Areas of Similar Figures How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures Work with a partner.

More information

Geometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles

Geometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.

More information

Investigating Relationships of Area and Perimeter in Similar Polygons

Investigating Relationships of Area and Perimeter in Similar Polygons Investigating Relationships of Area and Perimeter in Similar Polygons Lesson Summary: This lesson investigates the relationships between the area and perimeter of similar polygons using geometry software.

More information

Chapter 6. Similarity of Figures

Chapter 6. Similarity of Figures Chapter 6 Similarity of Figures 6.1 Similar Polygons 6.2 Determining if two Polygons are Similar 6.3 Drawing Similar Polygons 6.4 Similar Triangles 21 Name: 6.1 Similar Polygons A. What makes something

More information

A. 32 cu ft B. 49 cu ft C. 57 cu ft D. 1,145 cu ft. F. 96 sq in. G. 136 sq in. H. 192 sq in. J. 272 sq in. 5 in

A. 32 cu ft B. 49 cu ft C. 57 cu ft D. 1,145 cu ft. F. 96 sq in. G. 136 sq in. H. 192 sq in. J. 272 sq in. 5 in 7.5 The student will a) describe volume and surface area of cylinders; b) solve practical problems involving the volume and surface area of rectangular prisms and cylinders; and c) describe how changing

More information

Examples: 1. Write the angles in order from 2. Write the sides in order from

Examples: 1. Write the angles in order from 2. Write the sides in order from Lesson 1 Triangle Inequalities 17. I can apply the triangle inequalities theorems When considering triangles, two basic questions arise: Can any three sides form a triangle? What is the relationship between

More information

Geometry Regents Review

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

Therefore, x is 3. To find BC. find 2x or 2(3) = 6. Thus, BC is Linear Measure

Therefore, x is 3. To find BC. find 2x or 2(3) = 6. Thus, BC is Linear Measure Find the length of each line segment or object. 1. Refer to Page 18. The ruler is marked in centimeters. The tail of the fish starts at the zero mark of the ruler and the mouth appears to end 7 tenth marks

More information

Finding the Measure of Segments Examples

Finding the Measure of Segments Examples Finding the Measure of Segments Examples 1. In geometry, the distance between two points is used to define the measure of a segment. Segments can be defined by using the idea of betweenness. In the figure

More information

Topics Covered on Geometry Placement Exam

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

More information

Geometry Chapter 7. Ratios & Proportions Properties of Proportions Similar Polygons Similarity Proofs Triangle Angle Bisector Theorem

Geometry Chapter 7. Ratios & Proportions Properties of Proportions Similar Polygons Similarity Proofs Triangle Angle Bisector Theorem Geometry Chapter 7 Ratios & Proportions Properties of Proportions Similar Polygons Similarity Proofs Triangle Angle Bisector Theorem Name: Geometry Assignments Chapter 7 Date Due Similar Polygons Section

More information

Honors Geometry Final Exam Study Guide

Honors Geometry Final Exam Study Guide 2011-2012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.

More information

10-4 Inscribed Angles. Find each measure. 1.

10-4 Inscribed Angles. Find each measure. 1. Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semi-circle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what

More information

The common ratio in (ii) is called the scaled-factor. An example of two similar triangles is shown in Figure 47.1. Figure 47.1

The common ratio in (ii) is called the scaled-factor. An example of two similar triangles is shown in Figure 47.1. Figure 47.1 47 Similar Triangles An overhead projector forms an image on the screen which has the same shape as the image on the transparency but with the size altered. Two figures that have the same shape but not

More information

Warm Up. Use A ( 2, 3) and B (1, 0) 1. Find the slope of AB. 2. Find the midpoint of AB. 3. Find the distance of AB. 4. Simplify.

Warm Up. Use A ( 2, 3) and B (1, 0) 1. Find the slope of AB. 2. Find the midpoint of AB. 3. Find the distance of AB. 4. Simplify. Use A ( 2, 3) and B (1, 0) 1. Find the slope of AB. 2. Find the midpoint of AB. 3. Find the distance of AB. Warm Up 4. Simplify. 5. Draw an example of vertical angles. GOALS Develop and apply the

More information

3 rd Six Weeks

3 rd Six Weeks Geometry 3 rd Six Weeks 014-015 MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY Nov 9 10 11 1 13 6-1 Angle Measures in Polygons Class: Wksht #1 6- Properties of Parallelograms Class: Wksht # 6-3 Proving Parallelograms

More information

Warm-Up 3 Solutions. Peter S. Simon. October 13, 2004

Warm-Up 3 Solutions. Peter S. Simon. October 13, 2004 Warm-Up 3 Solutions Peter S. Simon October 13, 2004 Problem 1 An automobile insurance company has compiled data from a survey of 1000 16-year-old drivers during the year 2003. According to the results

More information

Perimeter, Circumference, and Area

Perimeter, Circumference, and Area -9 Perimeter, Circumference, and Area -9. Plan What You ll Learn To find perimeters of rectangles and squares, and circumferences of circles To find areas of rectangles, squares, and circles... And Why

More information

10.2 45-45 -90 Triangles

10.2 45-45 -90 Triangles Page of 6 0. --0 Triangles Goal Find the side lengths of --0 triangles. Key Words --0 triangle isosceles triangle p. 7 leg of a right triangle p. hypotenuse p. Geo-Activity Eploring an Isosceles Right

More information

Hands-On Mini Lab. Step 2 Pick one vertex and draw a segment to the opposite vertex. The angles of a quadrilateral have a special relationship.

Hands-On Mini Lab. Step 2 Pick one vertex and draw a segment to the opposite vertex. The angles of a quadrilateral have a special relationship. 10-7 Quadrilaterals MAIN IDEA I will classify quadrilaterals and find missing angle measures in quadrilaterals. New Vocabulary quadrilateral rectangle square ogram trapezoid Hands-On Mini Lab The figure

More information

5-1 Perpendicular and Angle Bisectors

5-1 Perpendicular and Angle Bisectors 5-1 Perpendicular and Angle Bisectors Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Construct each of the following. 1. A perpendicular bisector. 2. An angle bisector. 3. Find the midpoint and

More information

Thursday, January 12 / Friday, January 13. Student Objective (Obj. 3c) TSW identify and justify the congruency of two figures.

Thursday, January 12 / Friday, January 13. Student Objective (Obj. 3c) TSW identify and justify the congruency of two figures. Course: 7 th Grade Math Student Objective (Obj. 3c) TSW identify and justify the congruency of two figures. DETAIL LESSON PLAN Thursday, January 12 / Friday, January 13 Lesson 7-5 Congruent Figures Textbook

More information

Each pair of opposite sides of a parallelogram is congruent to each other.

Each pair of opposite sides of a parallelogram is congruent to each other. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite

More information

10-3 Area of Parallelograms

10-3 Area of Parallelograms 0-3 Area of Parallelograms MAIN IDEA Find the areas of parallelograms. NYS Core Curriculum 6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest,

More information

Chapter 8. Right Triangles

Chapter 8. Right Triangles Chapter 8 Right Triangles Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the

More information

7-3 Parallel and Perpendicular Lines

7-3 Parallel and Perpendicular Lines Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal. 7-3 Parallel Insert Lesson and Perpendicular Title Here Lines Vocabulary perpendicular lines parallel lines

More information

11-1 Areas of Parallelograms and Triangles. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary.

11-1 Areas of Parallelograms and Triangles. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 2. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. Each pair of opposite

More information

Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts:

Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Perimeter, Circumference, and Area Example 2: Find Perimeter

More information

Measuring Angles and Arcs

Measuring Angles and Arcs Then You measured angles and identified congruent angles. (Lesson 1-4) Now Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. Find arc lengths. New Vocabulary central

More information

Geometry Module 4 Unit 2 Practice Exam

Geometry Module 4 Unit 2 Practice Exam Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning

More information

7-1 Ratio and Proportion

7-1 Ratio and Proportion 7-1 Ratio and Proportion Ratio 1) Find the slope of line m provided that points and lie on m. 2) The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle? Proportion Cross

More information

Volume of Pyramids and Cones. Tape together as shown. Tape together as shown.

Volume of Pyramids and Cones. Tape together as shown. Tape together as shown. 7-6 Volume of Pyramids and Cones MAIN IDEA Find the volumes of pyramids and cones. New Vocabulary cone Math Online glencoe.com Extra Examples Personal Tutor Self-Check Quiz In this Mini Lab, you will investigate

More information

Trade of Metal Fabrication. Module 5: Pipe Fabrication Unit 9: Segmental Bends Phase 2

Trade of Metal Fabrication. Module 5: Pipe Fabrication Unit 9: Segmental Bends Phase 2 Trade of Metal Fabrication Module 5: Pipe Fabrication Unit 9: Segmental Bends Phase 2 Table of Contents List of Figures... 5 List of Tables... 5 Document Release History... 6 Module 5 Pipe Fabrication...

More information

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. A rhombus is a parallelogram with all four sides congruent. So, Then, is an isosceles triangle. Therefore, If a parallelogram

More information

THE DISTANCE FORMULA

THE DISTANCE FORMULA THE DISTANCE FORMULA In this activity, you will develop a formula for calculating the distance between any two points in a coordinate plane. Part 1: Distance Along a Horizontal or Vertical Line To find

More information

Properties of Special Parallelograms

Properties of Special Parallelograms Properties of Special Parallelograms Lab Summary: This lab consists of four activities that lead students through the construction of a parallelogram, a rectangle, a square, and a rhombus. Students then

More information

2nd Semester Geometry Final Exam Review

2nd Semester Geometry Final Exam Review Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular

More information

7-1 Ratios and Proportions

7-1 Ratios and Proportions 1. PETS Out of a survey of 1000 households, 460 had at least one dog or cat as a pet. What is the ratio of pet owners to households? The ratio of per owners to households is 23:50. 2. SPORTS Thirty girls

More information

8-3 Perimeter and Circumference

8-3 Perimeter and Circumference Learn to find the perimeter of a polygon and the circumference of a circle. 8-3 Perimeter Insert Lesson and Title Circumference Here perimeter circumference Vocabulary The distance around a geometric figure

More information

GEOMETRY (Common Core)

GEOMETRY (Common Core) GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Wednesday, August 12, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The

More information

Coordinate Algebra 1- Common Core Test -1. Diagnostic. Test. Revised 12/5/13 1:19 pm

Coordinate Algebra 1- Common Core Test -1. Diagnostic. Test. Revised 12/5/13 1:19 pm Coordinate Algebra 1- Common Core Test -1 Diagnostic Test Revised 12/5/13 1:19 pm 1. A B C is a dilation of triangle ABC by a scale factor of ½. The dilation is centered at the point ( 5, 5). Which statement

More information

Three-Dimensional Figures or Space Figures. Rectangular Prism Cylinder Cone Sphere. Two-Dimensional Figures or Plane Figures

Three-Dimensional Figures or Space Figures. Rectangular Prism Cylinder Cone Sphere. Two-Dimensional Figures or Plane Figures SHAPE NAMES Three-Dimensional Figures or Space Figures Rectangular Prism Cylinder Cone Sphere Two-Dimensional Figures or Plane Figures Square Rectangle Triangle Circle Name each shape. [triangle] [cone]

More information

as a fraction and as a decimal to the nearest hundredth.

as a fraction and as a decimal to the nearest hundredth. Express each ratio as a fraction and as a decimal to the nearest hundredth. 1. sin A The sine of an angle is defined as the ratio of the opposite side to the hypotenuse. So, 2. tan C The tangent of an

More information

Geometry CC Assignment #1 Naming Angles. 2. Complementary angles are angles that add up to degrees.

Geometry CC Assignment #1 Naming Angles. 2. Complementary angles are angles that add up to degrees. Geometry CC Assignment #1 Naming Angles 1. Name the given angle in 3 ways. A. Complementary angles are angles that add up to degrees. 3. Supplementary angles are angles that add up to degrees. #1 4. Given

More information

Coordinate Graphing and Geometric Constructions

Coordinate Graphing and Geometric Constructions HPTER 9 oordinate Graphing and Geometric onstructions hapter Vocabular coordinate plane origin graph image line of reflection rotation midpoint -ais ordered pair quadrants translation line smmetr rotational

More information

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 3. PROOF Write a two-column proof to prove that if ABCD is a rhombus with diagonal. 1. If, find. A rhombus is a parallelogram with all

More information

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

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

More information

5-1 Perpendicular and Angle Bisectors

5-1 Perpendicular and Angle Bisectors 5-1 Perpendicular and Angle Bisectors 5-1 Perpendicular and Angle Bisectors Warm Up Lesson Presentation Lesson Quiz Holt 5-1 Perpendicular and Angle Bisectors Warm Up Construct each of the following. 1.

More information

Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?

Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane

More information

http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4

http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4 of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the

More information

11-5 Areas of Similar Figures. For each pair of similar figures, find the area of the green figure. SOLUTION:

11-5 Areas of Similar Figures. For each pair of similar figures, find the area of the green figure. SOLUTION: The area of the green diamond 9 yd F each pair of similar figures, find the area of the green figure The scale fact between the blue triangle and the 1 green triangle The scale fact between the blue diamond

More information

GASOLINE The graph represents the cost of gasoline at $3 per gallon.

GASOLINE The graph represents the cost of gasoline at $3 per gallon. 9-6 Slope-Intercept Form MAIN IDEA Graph linear equations using the slope and -intercept. New Vocabular slope-intercept form -intercept Math Online glencoe.com Etra Eamples Personal Tutor Self-Check Quiz

More information

CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.

CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder. TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has

More information

Measuring Length and Area

Measuring Length and Area 11 Measuring Length and Area 11.1 Areas of Triangles and Parallelograms 11.2 Areas of Trapezoids, Rhombuses, and Kites 11.3 Perimeter and Area of Similar Figures 11.4 Circumference and Arc Length 11.5

More information

11-7 The Coordinate Plane

11-7 The Coordinate Plane 11-7 The Coordinate Plane MAIN IDEA Locate and graph ordered pairs on a coordinate plane. NYS Core Curriculum 6.G.10 Identif and plot points in all four quadrants. 6.CM.4 Share organized mathematical ideas

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

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 Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your

More information

Solve each equation by using models or a drawing. x = 3 Simplify. Check the solution. Since 2 (3) + 3 = 9, the solution is 3.

Solve each equation by using models or a drawing. x = 3 Simplify. Check the solution. Since 2 (3) + 3 = 9, the solution is 3. 3-5 Solving Two-Step Equations MAIN IDEA Solve two-step equations. New Vocabulary two-step equation Math Online glencoe.com Concepts In Motion Etra Eamples Personal Tutor Self-Check Quiz MONEY A florist

More information

Geometry Notes Chapter 12. Name: Period:

Geometry Notes Chapter 12. Name: Period: Geometry Notes Chapter 1 Name: Period: Vocabulary Match each term on the left with a definition on the right. 1. image A. a mapping of a figure from its original position to a new position. preimage B.

More information

24HourAnswers.com. Online Homework. Focused Exercises for Math SAT. Skill Set 12: Geometry - 2D Figures and 3D Solids

24HourAnswers.com. Online Homework. Focused Exercises for Math SAT. Skill Set 12: Geometry - 2D Figures and 3D Solids 24HourAnsers.com Online Homeork Focused Exercises for Math SAT Skill Set 12: Geometry - 2D Figures and 3D Solids Many of the problems in this exercise set came from The College Board, riters of the SAT

More information

Direct Variation. COMPUTERS Use the graph at the right that shows the output of a color printer.

Direct Variation. COMPUTERS Use the graph at the right that shows the output of a color printer. 9-5 Direct Variation MAIN IDEA Use direct variation to solve problems. New Vocabular direct variation constant of variation Math nline glencoe.com Etra Eamples Personal Tutor Self-Check Quiz CMPUTERS Use

More information

6-3 Tests for Parallelograms. Determine whether each quadrilateral is a parallelogram. Justify your answer.

6-3 Tests for Parallelograms. Determine whether each quadrilateral is a parallelogram. Justify your answer. 1. Determine whether each quadrilateral is a Justify your answer. 3. KITES Charmaine is building the kite shown below. She wants to be sure that the string around her frame forms a parallelogram before

More information

GEOMETRY (Common Core)

GEOMETRY (Common Core) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Tuesday, June 2, 2015 1:15 to 4:15 p.m. MODEL RESPONSE SET Table of Contents Question 25...................

More information

You can use the postulates below to prove several theorems.

You can use the postulates below to prove several theorems. Using Area Formulas You can use the postulates below to prove several theorems. AREA POSTULATES Postulate Area of a Square Postulate The area of a square is the square of the length of its side, or s.

More information

P.E.R.T. Math Study Guide

P.E.R.T. Math Study Guide A guide to help you prepare for the Math subtest of Florida s Postsecondary Education Readiness Test or P.E.R.T. P.E.R.T. Math Study Guide www.perttest.com PERT - A Math Study Guide 1. Linear Equations

More information

Pythagorean Theorem: 9. x 2 2

Pythagorean Theorem: 9. x 2 2 Geometry Chapter 8 - Right Triangles.7 Notes on Right s Given: any 3 sides of a Prove: the is acute, obtuse, or right (hint: use the converse of Pythagorean Theorem) If the (longest side) 2 > (side) 2

More information

Sample Test Questions

Sample Test Questions mathematics College Algebra Geometry Trigonometry Sample Test Questions A Guide for Students and Parents act.org/compass Note to Students Welcome to the ACT Compass Sample Mathematics Test! You are about

More information

LESSON 6.2 POLYNOMIAL OPERATIONS I

LESSON 6.2 POLYNOMIAL OPERATIONS I LESSON 6.2 POLYNOMIAL OPERATIONS I Overview In business, people use algebra everyday to find unknown quantities. For example, a manufacturer may use algebra to determine a product s selling price in order

More information

1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.

1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms. Quadrilaterals - Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals - Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,

More information

Geometry EOC Practice Test #3

Geometry EOC Practice Test #3 Class: Date: Geometry EOC Practice Test #3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which regular polyhedron has 12 petagonal faces? a. dodecahedron

More information

Circumference and Area of Circles

Circumference and Area of Circles ircumference and Area of ircles 7- MAIN IDEA Measure and record the distance d across the circular part of an object, such as a battery or a can, through its center. Find the circumference and area of

More information

10.1 Geometry Areas of Parallelograms, Triangles and Heron s Formula

10.1 Geometry Areas of Parallelograms, Triangles and Heron s Formula Name Due Date 4/10 https://www.youtube.com/watch?v=eh5zawhrioo 10.1 Geometry Areas of Parallelograms, Triangles and Heron s Formula Area of a Rectangle: A= Area of a Square: A= Area of a Parallelogram:

More information

Slope. SAFETY A ladder truck uses a moveable ladder to reach upper levels of houses and buildings.

Slope. SAFETY A ladder truck uses a moveable ladder to reach upper levels of houses and buildings. 9- MAIN IDEA Find the slope of a line. New Vocabular Slope SAFETY A ladder truck uses a moveable ladder to reach upper levels of houses and buildings. 1. The rate of change of the slope Math nline glencoe.com

More information

Honors Packet on. Polygons, Quadrilaterals, and Special Parallelograms

Honors Packet on. Polygons, Quadrilaterals, and Special Parallelograms Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 6-1) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386

More information

Summer Math Exercises. For students who are entering. Pre-Calculus

Summer Math Exercises. For students who are entering. Pre-Calculus Summer Math Eercises For students who are entering Pre-Calculus It has been discovered that idle students lose learning over the summer months. To help you succeed net fall and perhaps to help you learn

More information

Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.

Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular. CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes

More information

CHAPTER 7. Think & Discuss (p. 393) m Z 55 35 180. m Z 90 180. m Z 90 QR 2 RP 2 PQ 2 QR 2 10 2 12.2 2 QR 2 100 148.84 QR 2 48.84 AB 1 6 2 3 4 2 QR 7.

CHAPTER 7. Think & Discuss (p. 393) m Z 55 35 180. m Z 90 180. m Z 90 QR 2 RP 2 PQ 2 QR 2 10 2 12.2 2 QR 2 100 148.84 QR 2 48.84 AB 1 6 2 3 4 2 QR 7. HPTER 7 Think & Discuss (p. 393). The image in bo is flipped to get the image in bo. The image in bo is turned to get the image in bo D.. Sample answer: If ou look at the picture as a whole, the right

More information

Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources:

Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources: Geometry Honors: Extending 2 Dimensions into 3 Dimensions Semester 2, Unit 5: Activity 30 Resources: SpringBoard- Geometry Online Resources: Geometry Springboard Text Unit Overview In this unit students

More information

10.1 Areas of Quadrilaterals and triangles

10.1 Areas of Quadrilaterals and triangles 10.1 Areas of Quadrilaterals and triangles BASE AND HEIGHT MUST FORM A RIGHT ANGLE!! Draw the diagram, write the formula and SHOW YOUR WORK! FIND THE AREA OF THE FOLLOWING:. A rectangle with one side of

More information

13.3 Special Right Triangles

13.3 Special Right Triangles Name lass Date 13.3 Special Right Triangles Essential Question: What do you know about the side lengths and the trigonometric ratios in special right triangles? Eplore 1 Investigating an Isosceles Right

More information

Lesson 12.1 Skills Practice

Lesson 12.1 Skills Practice Lesson 12.1 Skills Practice Name Date Introduction to Circles Circle, Radius, and Diameter Vocabulary Define each term in your own words. 1. circle A circle is a collection of points on the same plane

More information

The Pythagorean Packet Everything Pythagorean Theorem

The Pythagorean Packet Everything Pythagorean Theorem Name Date The Pythagorean Packet Everything Pythagorean Theorem Directions: Fill in each blank for the right triangle by using the words in the Vocab Bo. A Right Triangle These sides are called the of

More information

Practice Test - Chapter 1. Use the figure to name each of the following.

Practice Test - Chapter 1. Use the figure to name each of the following. Use the figure to name each of the following. 1. the line that contains points Q and Z The points Q and Z lie on the line b, line b 2. two points that are coplanar with points W, X, and Y Coplanar points

More information

Building Blocks of Geometry

Building Blocks of Geometry Page 1 of 10 L E S S O N 1.1 Nature s Great Book is written in mathematical symbols. GALILEO GALILEI Building Blocks of Geometry Three building blocks of geometry are points, lines, and planes. A point

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.

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

Multiplying a Binomial by a Monomial

Multiplying a Binomial by a Monomial Looking 4 Ahead Then You have already multiplied monomials. (Lesson 9-3) Now Use models to multiply a binomial by a monomial. Multiply a binomial by a monomial to solve equations. New Vocabulary binomal

More information

RAVEN S GUIDE TO BRITISH COLUMBIA LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND

RAVEN S GUIDE TO BRITISH COLUMBIA LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND RAVEN S GUIDE TO BRITISH COLUMBIA MATHEMATICS GRADE 6 LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND STUDENT GUIDE AND RESOURCE BOOK Key to Student Success

More information

11-4 Areas of Regular Polygons and Composite Figures

11-4 Areas of Regular Polygons and Composite Figures 1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,

More information

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

More information

Number Sense and Operations

Number Sense and Operations Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

More information

CHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms

CHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 6-1) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 1-7 HW: Pgs: 8-10 DAY 2: (6-2) Pgs:

More information

3. If AC = 12, CD = 9 and BE = 3, find the area of trapezoid BCDE. (Mathcounts Handbooks)

3. If AC = 12, CD = 9 and BE = 3, find the area of trapezoid BCDE. (Mathcounts Handbooks) EXERCISES: Triangles 1 1. The perimeter of an equilateral triangle is units. How many units are in the length 27 of one side? (Mathcounts Competitions) 2. In the figure shown, AC = 4, CE = 5, DE = 3, and

More information

SAT Math Hard Practice Quiz. 5. How many integers between 10 and 500 begin and end in 3?

SAT Math Hard Practice Quiz. 5. How many integers between 10 and 500 begin and end in 3? SAT Math Hard Practice Quiz Numbers and Operations 5. How many integers between 10 and 500 begin and end in 3? 1. A bag contains tomatoes that are either green or red. The ratio of green tomatoes to red

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 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

Test to see if ΔFEG is a right triangle.

Test to see if ΔFEG is a right triangle. 1. Copy the figure shown, and draw the common tangents. If no common tangent exists, state no common tangent. Every tangent drawn to the small circle will intersect the larger circle in two points. Every

More information

The scale factor between the blue triangle and the green triangle is

The scale factor between the blue triangle and the green triangle is For each pair of similar figures, find the area of the green figure 1 SOLUTION: The scale factor between the blue diamond and the green diamond is 2 The area of the green diamond is 9 yd 2 SOLUTION: The

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.

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

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,

More information