Chapter 9 Resource Masters

Transcription

1 Chapter 9 Resource Masters

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3 Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Study Guide and Intervention Workbook Study Guide and Intervention Workbook (Spanish) Skills Practice Workbook Skills Practice Workbook (Spanish) Practice Workbook Practice Workbook (Spanish) Answers for Workbooks The answers for Chapter 9 of these workbooks can be found in the back of this Chapter Resource Masters booklet. Spanish Assessment Masters Spanish versions of forms 2A and 2C of the Chapter 9 Test are available in the Pre-Algebra Spanish Assessment Masters ( ). Copyright by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teacher, and families without charge; and be used solely in conjunction with Glencoe Pre-Algebra. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH ISBN: Pre-Algebra Chapter 9 Resource Masters

4 CONTENTS Vocabulary Builder...vii Lesson 9-1 Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson 9-2 Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson 9-3 Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson 9-4 Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson 9-5 Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson 9-7 Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson 9-8 Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Chapter 9 Assessment Chapter 9 Test, Form Chapter 9 Test, Form 2A Chapter 9 Test, Form 2B Chapter 9 Test, Form 2C Chapter 9 Test, Form 2D Chapter 9 Test, Form Chapter 9 Open-Ended Assessment Chapter 9 Vocabulary Test/Review Chapter 9 Quizzes 1 & Chapter 9 Quizzes 3 & Chapter 9 Mid-Chapter Test Chapter 9 Cumulative Review Chapter 9 Standardized Test Practice Standardized Test Practice Student Recording Sheet...A1 ANSWERS...A2 A31 Lesson 9-6 Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment iii

5 Teacher s Guide to Using the Chapter 9 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 9 Resource Masters includes the core materials needed for Chapter 9. These materials include worksheets, etensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing in the Pre-Algebra TeacherWorks CD-ROM. Vocabulary Builder Pages vii-viii include a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or eamples for each term. You may suggest that students highlight or star the terms with which they are not familiar. When to Use Give these pages to students before beginning Lesson 9-1. Encourage them to add these pages to their Pre-Algebra Study Notebook. Remind them to add definitions and eamples as they complete each lesson. Study Guide and Intervention Each lesson in Pre-Algebra addresses one or two objectives. There is one Study Guide and Intervention master for each lesson. When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent. Skills Practice There is one master for each lesson. These provide computational practice at a basic level. When to Use These masters can be used with students who have weaker mathematics backgrounds or need additional reinforcement. Practice There is one master for each lesson. These problems more closely follow the structure of the Practice and Apply section of the Student Edition eercises. These eercises are of average difficulty. When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson. Reading to Learn Mathematics One master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the contet of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques. When to Use This master can be used as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students. Enrichment There is one etension master for each lesson. These activities may etend the concepts in the lesson, offer an historical or multicultural look at the concepts, or widen students perspectives on the mathematics they are learning. These are not written eclusively for honors students, but are accessible for use with all levels of students. When to Use These may be used as etra credit, short-term projects, or as activities for days when class periods are shortened. iv

6 Assessment Options The assessment masters in the Chapter 9 Resource Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use. Chapter Assessment Chapter Tests Form 1 contains multiple-choice questions and is intended for use with basic level students. Forms 2A and 2B contain multiple-choice questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Forms 2C and 2D are composed of freeresponse questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Grids with aes are provided for questions assessing graphing skills. Form 3 is an advanced level test with free-response questions. Grids without aes are provided for questions assessing graphing skills. All of the above tests include a freeresponse Bonus question. The Open-Ended Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment. A Vocabulary Test, suitable for all students, includes a list of the vocabulary words in the chapter and ten questions assessing students knowledge of those terms. This can also be used in conjunction with one of the chapter tests or as a review worksheet. Intermediate Assessment Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and free-response questions. Continuing Assessment The Cumulative Review provides students an opportunity to reinforce and retain skills as they proceed through their study of Pre-Algebra. It can also be used as a test. This master includes free-response questions. The Standardized Test Practice offers continuing review of pre-algebra concepts in various formats, which may appear on the standardized tests that they may encounter. This practice includes multiplechoice, grid-in, and open-ended questions. Bubble-in and grid-in answer sections are provided on the master. Answers Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages This improves students familiarity with the answer formats they may encounter in test taking. The answers for the lesson-by-lesson masters are provided as reduced pages with answers appearing in red. Full-size answer keys are provided for the assessment masters in this booklet. v

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8 9 NAME DATE PERIOD Reading to Learn Mathematics Vocabulary Builder This is an alphabetical list of key vocabulary terms you will learn in Chapter 9. As you study this chapter, complete each term s definition or description. Remember to add the page number where you found the term. Add these pages to your Pre-Algebra Study Notebook to review vocabulary at the end of the chapter. Vocabulary Term Found on Page Definition/Description/Eample Vocabulary Builder acute angle angle congruent kuhn-groo-uhnt degree Distance Formula equilateral triangle EE-kwuh-LAT-uh-ruhl hypotenuse hy-paht-uhn-noos isosceles triangle eye-sahs-uh-leez Midpoint Formula vii

9 9 NAME DATE PERIOD Reading to Learn Mathematics Vocabulary Builder (continued) Vocabulary Term obtuse angle ahb-toos Found on Page Definition/Description/Eample protractor Pythagorean Theorem puh-thag-uh-ree-uhn real numbers right angle scalene triangle SKAY-LEEN similar triangles square root straight angle trigonometric ratio TRIHG-uh-nuh-MEH-trihk verte viii

10 9-1 Study Guide and Intervention Squares and Square Roots Squares and Square Roots A perfect square is the square of a whole number. A square root of a number is one of two equal factors of the number. Every positive number has a positive square root and a negative square root. The square root of a negative number such as 25, is not real because the square of a number is never negative. Eample 1 a. 144 Find each square root. 144 indicates the positive square root of 144. Since , b indicates the negative square of 121. Since , Lesson 9-1 c. 4 4 indicates both square roots of 4. Since 2 2 4, 4 2 and 4 2 Eample 2 Use a calculator to find 34 to the nearest tenth. 2nd ENTER Use a calculator Round to the nearest tenth. Eercises Find each square root not poss not poss. 11. ± Use a calculator to find each square root to the nearest tenth Glencoe/McGraw-Hill 489 Glencoe Pre-Algebra

11 9-1 Skills Practice Squares and Square Roots Find each square root, if possible not possible not possible Use a calculator to find each square root to the nearest tenth not possible Estimate each square root to the nearest whole number. Do not use a calculator Glencoe/McGraw-Hill 490 Glencoe Pre-Algebra

12 9-1 Practice Squares and Square Roots Find each square root, if possible not possible not possible Use a calculator to find each square root to the nearest tenth Find the negative square root of 840 to the nearest tenth If 2 476, what is the value of to the nearest tenth? Lesson The number 22 lies between which two consecutive whole numbers? Do not use a calculator. 4 and 5 Estimate each square root to the nearest whole number. Do not use a calculator GEOMETRY A square tarpaulin covering a softball field has an area of 441 m 2. What is the length of one side of the tarpaulin? 21 m 38. MONUMENTS Refer to Eample 4 on page 438 of your tetbook. The highest observation deck on the Eiffel Tower in Paris is about 899 feet above the ground. About how far could a visitor see on a clear day? about 36.6 mi Glencoe/McGraw-Hill 491 Glencoe Pre-Algebra

13 9-1 Reading to Learn Mathematics Squares and Square Roots Pre-Activity How are square roots related to factors? Do the activity at the top of page 436 in your tetbook. Write your answers below. Reading the Lesson a. Describe the difference between the first four and the last four values of. The first four are whole numbers and the last four are not. b. Eplain how you found an eact answer for the first four values of. To find an eact answer, determine what number times itself is equal to each value of. c. How did you find an estimate for the last four values of? Choose a decimal value that, when multiplied by itself, is approimately equal to the value of See students work. Write a definition and give an eample of each new vocabulary word or phrase. Vocabulary Definition Eample 1. perfect square 2. square root 3. radical sign Helping You Remember 4. For each number in the table, tell whether it has a real square root and eplain why or why not. Then indicate if the number is a perfect square and eplain. Real Square Root? Perfect Square? 26 Yes; positive number No; not the square of a whole number 81 No; negative number 256 Yes; positive number Yes; square of Yes; positive number Yes; square of 38 5 No; negative number Glencoe/McGraw-Hill 492 Glencoe Pre-Algebra

14 9-1 Enrichment Roots The symbol 00 indicates a square root. By placing a number in the upper left, the symbol can be changed to indicate higher roots because because , because ,000 Find each of the following Lesson ,000, ,000, Glencoe/McGraw-Hill 493 Glencoe Pre-Algebra

15 9-2 Study Guide and Intervention The Real Number System The set of real numbers consists of all natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Rational numbers can be written as fractions. Irrational numbers are decimals that do not repeat or terminate. Rational Numbers Integers 1 Whole 5 Numbers 0 Natural Numbers Irrational Numbers Eample a. 7 b. 0.6 This number is a natural number, a whole number, an integer, and a rational number. This repeating decimal is a rational number because it is equivalent to 2 3. c. 71 It is not the square root of a perfect square so it is irrational. d Since 8 1 = 27, this number is an integer and a rational number. 3 e. 169 Because 169 = 13, this number is an integer and a rational number. Eercises Name all of the sets of numbers to which each real number belongs. Let N natural numbers, W whole numbers, Z integers, Q rational numbers, and I irrational numbers N, W, Z, Q I 3. Q Z, Q N, W, Z, Q 6. O W, Z, Q Q Q N, W, Z, Q Name all of the sets of numbers to which each real number belongs. Q 11. I Z, Q Q Q Z, Q Glencoe/McGraw-Hill 494 Glencoe Pre-Algebra

16 9-2 Skills Practice The Real Number System Name all of the sets of numbers to which each real number belongs. Let N natural numbers, W whole numbers, Z integers, Q rational numbers, and I irrational numbers N, W, Z, Q N, W, Z, Q 3. 5 Z, Q Q 5. 1 Q Q I 8. 7 I N, W, Z, Q Z, Q Q Q N, W, Z, Q W, Z, Q I Determine whether each statement is sometimes, always, or never true. 16. A whole number is a rational number. always 17. A rational number is a natural number. sometimes 18. A negative number is an integer. sometimes 19. Zero is a natural number. never Lesson 9-2 Replace each with,, or to make a true statement Order each set of numbers from least to greatest , 5.3, 28, , 28 4, 5.3, , 7 1 4, 3 6, , 7 1, 7.27, , 72.25, 9, , 9, 9, ALGEBRA Solve each equation. Round to the nearest tenth, if necessary. 29. a d f g h k b y m Glencoe/McGraw-Hill 495 Glencoe Pre-Algebra

17 9-2 Practice The Real Number System Name all of the sets of numbers to which each real number belongs. Let N natural numbers, W whole numbers, Z integers, Q rational numbers, and I irrational numbers N, W, Z, Q Z, Q Q 4. 1 Q Q 6. 8 I I N, W, Z, Q 9. 2 Z, Q Q Q I Determine whether each statement is sometimes, always, or never true. 13. A decimal number is an irrational number. sometimes 14. An integer is a whole number. sometimes 15. A natural number is an integer. always 16. A negative integer is a natural number. never Replace each with,, or to make a true statement Order each set of numbers from least to greatest , 6.9 1, 7 1 8, , 49, , , 43, , 4.13, 4.13, 4 1, , 1.5, 1, 6 6, 2, 1, ALGEBRA Solve each equation. Round to the nearest tenth, if necessary. 26. h k c t u w GARDENING Ray planted a square garden that covers an area of 200 ft 2. How many feet of fencing does he need to surround the garden? 56.6 ft Glencoe/McGraw-Hill 496 Glencoe Pre-Algebra

18 9-2 Reading to Learn Mathematics The Real Number System Pre-Activity How can squares have lengths that are not rational numbers? Do the activity at the top of page 441 in your tetbook. Write your answers below. a. The small square at the right has an area of 1 square unit. Find the area of the shaded triangle. 1 2 units2 b. Suppose eight triangles are arranged as shown. What shape is formed by the shaded triangles? square c. Find the total area of the four shaded triangles. 2 square units d. What number represents the length of the side of the shaded square? 2 Reading the Lesson 1 2. See students work. Write a definition and give an eample of each new vocabulary word or phrase. Lesson 9-2 Vocabulary Definition Eample 1. irrational numbers 2. real numbers Choose the correct term to complete each sentence. 3. Numbers with decimals that are not repeating or terminating (are, are not) irrational numbers. 4. All square roots (are, are not) irrational numbers. 5. Irrational numbers (are, are not) real numbers. Helping You Remember 6. Fill in the missing terms on the following diagram. Then fill in the remaining blanks with eamples of each type of number. Use numbers different than those in your tetbook. Sample eamples are given Integers Numbers 1 Whole Numbers 7 0 Numbers 8 Numbers 3 Numbers Glencoe/McGraw-Hill 497 Glencoe Pre-Algebra

19 9-2 Enrichment Diagonals To find the length of diagonals in cubes and rectangular solids, a formula can be applied. In the eample below, the length of diagonal A G, or d, can be found using the formula d 2 a 2 b 2 c 2 or d a 2 b 2. c 2 Eample 1 A F B d D C c G The diagonal, d, is equal to the square root of the sum of the squares of the length, a, the width, b, and the height, c. a E b H Eample 2 Find the length of the diagonal of a rectangular prism with length of 8 meters, width of 6 meters, and height of 10 meters. d m Substitute the dimensions into the equation. Square each value. Add. Find the square root of the sum. Round the answer to the nearest tenth. Solve. Use d a 2 b 2 c 2. Round answers to the nearest tenth. 1. Find the diagonal of a cube with sides of 6 inches in. 2. Find the diagonal of a cube with sides of 2.4 meters. 4.2 m 3. Find the diagonal of a rectangular solid with length of 18 meters, width of 16 meters, and height of 24 meters. 34 m 4. Find the diagonal of a rectangular solid with length of 15.1 meters, width of 8.4 meters, and height of 6.3 meters m 5. Find the diagonal of a cube with sides of 34 millimeters mm 6. Find the diagonal of a rectangular solid with length of 8.9 millimeters, width of 6.7 millimeters, and height of 14 millimeters mm Glencoe/McGraw-Hill 498 Glencoe Pre-Algebra

20 9-3 Study Guide and Intervention Angles Measuring and Drawing Angles An angle is made up of two rays that have a common endpoint, called the verte. The most common unit of measure for angles is the degree. There are 360 in a circle. Angles are measured using protractors. Eample 1 a. Use a protractor to measure ABC A m ABC is 65. b. Draw D having a measure of B C D Classifying Angles Angles are classified by their degree measure. Acute angles measure between 0 and 90. A right angle measures 90. An obtuse angle measures between 90 and 180. A straight angle measures 180. Eample 2 a. B b. c. G D F A Eercises C m ABC = 90 So, ABC is right. Classify each angle as acute, obtuse, right, or straight. Use protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or straight. 1. AHB 30 acute 2. BHD 60 acute 3. AHD 90 right 4. AHE 98 obtuse 5. AHF 135 obtuse 6. AHG 180 straight E 30 m ABC 90 So, ABC is acute. H 150 m ABC 90 So, ABC is obtuse. A B C D H E I F G Lesson 9-3 Use a protractor to draw an angle having each measurement. Then classify each angle as acute, obtuse, right, or straight acute acute Glencoe/McGraw-Hill 499 Glencoe Pre-Algebra

21 9-3 Skills Practice Angles Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or straight. 1. AHB 20 ; acute 2. AHC 55 ; acute 3. AHD 90 ; right 4. AHE 120 ; obtuse 5. AHF 165 ; obtuse 6. AHG 180 ; straight 7. BHD 70 ; acute 8. DHG 90 ; right 9. CHE 65 ; acute 10. CHF 110 ; obtuse 11. DHF 75 ; acute 12. BHF 145 ; obtuse D C E F B A H G Use a protractor to draw an angle having each measurement. Then classify each angle as acute, obtuse, right, or straight acute acute Glencoe/McGraw-Hill 500 Glencoe Pre-Algebra

22 9-3 Practice Angles Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or straight. 1. MTN 10 ; acute 2. MTO 50 ; acute 3. MTP 90 ; right 4. MTQ 125 ; obtuse 5. MTR 140 ; obtuse 6. NTO 40 ; acute 7. MTS 180 ; straight 8. NTP 80 ; acute 9. PTS 90 ; right 10. QTR 15 ; acute P Q O R N M T S Use a protractor to draw an angle having each measurement. Then classify each angle as acute, obtuse, right, or straight acute acute Lesson 9-3 POPULATION For Eercises 17 19, use the graphic shown. 17. Classify each angle in the circle graph as acute, obtuse, right, or straight. 0-9: acute, 10-19: acute, 20-44: obtuse, 45-64: acute, 65-79: acute, 80 : acute 18. Find the measure of each angle of the circle graph. 0-9: 75, 10-19: 69, 20-44: 135, 45-64: 57, 65-79: 20, 80 : If the world population in 1998 was 5,926,062,000, how many people were years old. 1,125,951,780 World Population by Age, % % % % 80 1% % Glencoe/McGraw-Hill 501 Glencoe Pre-Algebra

23 9-3 NAME DATE PERIOD Reading to Learn Mathematics Angles Pre-Activity How are angles used in circle graphs? Do the activity at the top of page 447 in your tetbook. Write your answers below. a. Which method did half of the voters prefer? in booths Reading the Lesson b. Suppose 100 voters were surveyed. How many more voters preferred to vote in booths than on the Internet? 26 c. Each section of the graph shows an angle. A straight angle resembles a line. Which section shows a straight angle? in booths See students work. Write a definition and give an eample of each new vocabulary word or phrase. Vocabulary Definition Eample 1. point 2. ray 3. line 4. angle 5. verte 6. side 7. degree 8. protractor 9. acute angle 10. right angle 11. obtuse angle 12. straight angle Helping You Remember 13. Label the parts of the angles below and classify each as acute, right, obtuse, or straight. 100 obtuse angle A acute angle AB C B 35 C Glencoe/McGraw-Hill 502 Glencoe Pre-Algebra

24 9-3 Enrichment Angle Relationships Angles are measured in degrees ( ). Each degree of an angle is divided into 60 minutes ( ), and each minute of an angle is divided into 60 seconds ( ) Two angles are complementary if the sum of their measures is 90. Find the complement of each of the following angles Two angles are supplementary if the sum of their measures is 180. Find the supplement of each of the following angles Lesson 9-3 Glencoe/McGraw-Hill 503 Glencoe Pre-Algebra

25 9-4 Study Guide and Intervention Triangles Angles of a Triangle The sum of the measures of the angles of a triangle is 180. Eample 1 Find the value of in DEF. m D m E m F 180 The sum of the measures is m D 43 and m E Simplify Subtract 95 from each side. E 52 D 43 F Classifying Triangles Triangles are classified by their angles or by their sides. Acute triangles have all acute angles. Obtuse triangles have one obtuse angle. Right triangles have one right angle. Scalene triangles have no congruent sides. Isosceles triangles have at least two sides congruent. Equilateral triangles have all sides congruent. Eample 2 STU has all acute angles. Classify the triangle by its angles and by its sides. STU has no two sides that are congruent. So, STU is an acute scalene triangle. U 50 S T Eercises Find the value of in each triangle. Then classify each triangle as acute, right, or obtuse ; obtuse ; acute 68 ; right Classify each triangle by its angles and by its sides right, scalene obtuse, isosceles acute, equilateral Glencoe/McGraw-Hill 504 Glencoe Pre-Algebra

26 9-4 Skills Practice Triangles Find the value of in each triangle. Then classify each triangle as acute, right, or obtuse ; acute ; right ; obtuse ; acute ; acute ; right ; obtuse ; acute ; acute ; acute Classify each dashed triangle by its angles and by its sides right, scalene acute, isosceles obtuse, scalene Lesson acute, isosceles obtuse, scalene acute, equilateral Glencoe/McGraw-Hill 505 Glencoe Pre-Algebra

27 9-4 Practice Triangles Find the value of in each triangle. Then classify each triangle as acute, right, or obtuse ; acute ; obtuse ; acute ; acute ; right ; acute ; obtuse ; acute ; right ; right ALGEBRA The measures of the angles of a triangle are in the ratio 5:6:9. What is the measure of each angle? 45, 54, ALGEBRA Determine the measures of the angles of MNO if the measures of the angles are in the ratio 2:4:6. 30, 60, Classify each triangle by its angles and by its sides acute, scalene right, isosceles obtuse, isosceles acute, equilateral Glencoe/McGraw-Hill 506 Glencoe Pre-Algebra

28 9-4 Reading to Learn Mathematics Triangles Pre-Activity How do the angles of a triangle relate to each other? Do the activity at the top of page 453 in your tetbook. Write your answers below. a d. See students work. a. Use a straightedge to draw a triangle on a piece of paper. Then cut out the triangle and label the vertices X, Y, and Z. b. Fold the triangle as shown so that point Z lies on side XY as shown. Label Z as 2. c. Fold again so point X meets the verte of 2. Label X as 1. d. Fold so point Y meets the verte of 2. Label Y as 3. e. Make a conjecture about the sum of the measures of 1, 2, and 3. Eplain your reasoning. The sum of the measures is 180. Reading the Lesson See students work. Write a definition and give an eample of each new vocabulary word or phrase. Vocabulary Definition Eample 1. line segment 2. verte 3. acute triangle 4. obtuse triangle 5. right triangle 6. congruent 7. scalene triangle 8. isosceles triangle Lesson equilateral triangle Helping You Remember 10. Describe an obtuse, scalene triangle. a triangle with one obtuse angle and no congruent sides 11. Describe an equilateral triangle. all angles and sides are congruent Glencoe/McGraw-Hill 507 Glencoe Pre-Algebra

29 9-4 Enrichment Using Proportions to Approimate Height A proportion can be used to determine the height of tall structures if three variables of the proportion are known. The three known variables are usually the height, a, of the observer, the length, b, of the observer s shadow, and the length, d, of the structure s shadow. However, a proportion can be solved given any three of the four variables. a c a b c d b d This chart contains information about various observers and tall buildings. Use proportions and your calculator to complete the chart of tall buildings of the world. Height of Length of Building Height of Length of Observer Shadow Location Building Shadow ft 8 in. Natwest, London 600 ft 80 ft 4 ft 9 in. 19 in. Columbia Seafirst Center, Seattle 954 ft 318 ft 5 ft 10 in. 14 in. Wachovia building, Winston-Salem 410 ft 82 ft 6 ft 15 in. Waterfront Towers, Honolulu 400 ft 83 ft 4 in. 6 ft 1 ft CN Tower, Toronto 1821 ft 303 ft 6 in. 5 ft 9 in. 1 ft 11 in. Gateway Arch, St. Louis 630 ft 210 ft 5 ft 3 in. 1 ft 9 in. Eiffel Tower, Paris 984 ft 328 ft 4 ft 8 in. Teas Commerce Tower, Houston 1002 ft 167 ft 5 ft 6 in. 11 in. John Hancock Tower, Boston 790 ft 131 ft 8 in. 5 ft 4 in. 8 in. Sears Tower, Chicago 1454 ft 181 ft 9 in. 5 ft 6 in. 11 in. Barnett Tower, Jacksonville 631 ft 105 ft 2 in. Glencoe/McGraw-Hill 508 Glencoe Pre-Algebra

30 9-5 Study Guide and Intervention The Pythagorean Theorem Pythagorean Theorem Words If a triangle is a right triangle, then the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Model c Symbols c 2 a 2 b 2 a b Eample c 2 a 2 + b 2 Find the length of the hypotenuse of the right triangle. Pythagorean Theorem c Replace a with 16 and b with 30. c Evaluate 16 2 and c Add 256 and 900. c c 34 Take the square root of each side. Simplify. The length of the hypotenuse is 34 cm. 16 cm 30 cm c cm Eercises Find the length of the hypotenuse in each right triangle. Round to the nearest tenth if necessary. 15 in in c m c ft 43.0 c in. 11 m If c is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. 4. a = 18, b = 80, c =? a =?, b = 70, c = a = 14, b =?, c = a =?, b = 48, c = The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle. 8. a = 16, b = 30, c = 34 yes 9. a = 25, b = 31, c = 37 no 12 m 35 ft 25 ft 10. a = 21, b = 29, c = 42 no Lesson 9-5 Glencoe/McGraw-Hill 509 Glencoe Pre-Algebra

31 9-5 Skills Practice The Pythagorean Theorem Find the length of the hypotenuse in each right triangle. Round to the nearest tenth, if necessary ft in yd cm 9.3 c m 3.1 m 24 in. 16 yd 4.2 m c in. c yd 8 ft c m 5.4 cm 10 m c ft 9 m c cm If c is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. 7. a?, b 24, c a 16, b?, c a 24, b?, c a 5, b?, c a?, b 32, c a 21, b?, c a 18, b 29, c? a?, b 36, c a 8, b?, c a 14, b 21, c? a?, b 30, c a 4, b?, c a 13, b 18, c? a?, b 55, c The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle m, 5 m, 4 m no in., 4 in., 5 in. yes Glencoe/McGraw-Hill 510 Glencoe Pre-Algebra

32 9-5 Practice The Pythagorean Theorem Find the length of the hypotenuse in each right triangle. Round to the nearest tenth, if necessary ft c ft c m 30 m 20 ft 16 m in ft in. c in. c ft 7.3 ft c cm c in in cm 12.2 cm 58.6 in. If c is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth, if necessary. 7. a?, b 15, c a 8, b?, c a 11, b 16, c? a?, b 13, c a 10, b?, c a 21, b 23, c? a?, b 27, c a 48, b?, c a 26, b 596, c? a?, b 12, c The lengths of three sides of a triangle are given. Determine whether each triangle is a right triangle m, 5 m, 10 m no in., 12 in., 15 in. yes 19. ARCHITECTURE The diagonal distance covered by a flight of stairs is 21 ft. If the stairs cover 10 ft horizontally, how tall are they? 18.5 ft 20. KITES A kite is flying at the end of a 300-foot string. It is 120 feet above the ground. About how far away horizontally is the person holding the string from the kite? ft Lesson 9-5 Glencoe/McGraw-Hill 511 Glencoe Pre-Algebra

33 9-5 NAME DATE PERIOD Reading to Learn Mathematics The Pythagorean Theorem Pre-Activity How do the sides of a right triangle relate to each other? Do the activity at the top of page 460 in your tetbook. Write your answers below. a. Find the area of each square. 9 units 2 ; 16 units 2 ; 25 units 2 b. What relationship eists among the areas of the squares? The area of the large square is equal to the sum of the areas of the two smaller squares. c. Draw three squares with sides 5, 12, and 13 units so that they form a right triangle. What relationship eists among the areas of these squares? The area of the large square is equal to the sum of the areas of the two smaller squares. Reading the Lesson 1 5. See students work. Write a definition and give an eample of the new vocabulary word or phrase. Vocabulary Definition Eample 1. legs 2. hypotenuse 3. Pythagorean Theorem 4. solving a right triangle 5. converse Helping You Remember 6. Write out in words the steps for solving the right triangle shown. c 2 a 2 + b 2 Pythagorean Theorem 22 2 a Replace c with 22 and b with a Evaluate 22 2 and a Subtract 400 from each side. 84 a 2 Simplify. 84 a 2 a 9.2 Take the square root of each side. The length of the leg is about 9.2 units a Glencoe/McGraw-Hill 512 Glencoe Pre-Algebra

34 9-5 Enrichment Pythagorean Theorem Use the Pythagorean Theorem to find the area of the shaded region in the figure at the right. Think of the figure as four triangles and a square. Think of the figure as a large square. a b a b b c c a a a a c c b b b b a a b area of the 4 triangles area of the center square area of large square a b c 2 a 2 a b b 2 a b 2 a b c 2 a 2 b 2 a b a b 2 a b c 2 a 2 b 2 2 a b 2 a b c 2 2 a b a 2 b 2 c 2 a 2 b 2 The relationship c 2 a 2 b 2 is true for all right triangles. Use the Pythagorean Theorem to find the area of A, B, and C in each of the following. Then, answer true or false for the statement A B C C 3. C C A 3 5 A 9 Squares B A Equilateral Triangles B Semicircles A: 81, A: , A: 1.125, B: 144, B: 4 3, B: 2.000, C: 225; true C: ; true C: ; true B Lesson 9-5 Glencoe/McGraw-Hill 513 Glencoe Pre-Algebra

35 9-6 Study Guide and Intervention The Distance and Midpoint Formulas Distance and Midpoint Formulas On a coordinate plane, the distance d between two points with coordinates ( 1, y 1 ) and ( 2, y 2 ) is given by d ( 2 1 ) 2 ( y 2. y 1 ) 2 The midpoint of a line 1 segment whose endpoints are ( 1, y 1 ) and ( 2, y 2 ) is given by, y y 2 Eample Find the distance between M(8, 1) and N ( 2, 3). Round to the nearest tenth, if necessary. Then find the coordinates of the midpoint of M N. d ( 2 1 ) 2 ( y 2 y 1 ) 2 Distance Formula MN (8 ( 2)) 2 (1 3) 2 MN (10) 2 2) ( 2 ( 2, y 1 ) (2, 3), ( 2, y 2 ) (8, 1) Simplify. MN Evaluate 10 2 and ( 2) 2. MN 104 Add 100 and 4. MN 10.2 Take the square root. (2, 3) N O (8, 1) M The distance between points M and N is about 10.2 units. 1 midpoint, 2 y 1 y Midpoint Formula ( 2) 8, Substitution (3, 2) Simplify. The coordinates of the midpoint of M N are (3, 2). Eercises Find the distance between each pair of points. Round the nearest tenth, if necessary. 1. A (3, 1), B (2,5) C ( 2, 4), D (3, 7) E (5, 3), F (4,2) G ( 6, 5), H ( 4, 3) I ( 4, 3), J(4,4) K (5, 0), L ( 2, 1) M (2,1), N (6,5) O (0,0), P ( 5, 6) 7.8 The coordinates of the endpoints of a segment are given. Find the coordinates of the midpoint of each segment. 9. Q (3, 5), R (4, 2) (3.5, 3.5) 10. S ( 6, 4), T ( 5, 6) ( 5.5, 1) 11. U (2, 1), V (4, 4) (3, 2.5) 12. W (5, 1), X ( 2, 1) (1.5, 0) 13. Y ( 5, 3), Z (2, 5) ( 1.5, 1) 14. A (8, 1), B (3, 1) (5.5, 1) 15. C (0, 0), D (2, 4) (1, 2) 15. E ( 5, 3), F (4, 7) ( 0.5, 5) Glencoe/McGraw-Hill 514 Glencoe Pre-Algebra

36 9-6 Skills Practice The Distance and Midpoint Formulas Find the distance between each pair of points. Round to the nearest tenth, if necessary. 1. A(2, 4), B(1, 3) P(5, 10), Q( 1, 1) G(3, 1), H(5, 6) C( 2, 6), D( 7, 1) E( 6, 2), F(4, 1) J( 5, 3), K(4, 2) M( 5, 5), N(3, 4) V(4, 7), W(1, 6) X(4, 6), Y( 3, 7) R(0, 0), S( 1, 1) T (7, 3), U( 2, 2) A(6, 2), B(1, 3) 5.1 Lesson 9-6 GEOMETRY Find the perimeter of each figure. y (1, 6) E y 22.7 B (3, 6) A (4, 1) D (5, 0) O C (0, 0) O F (1, 3) The coordinates of the endpoints of a segment are given. Find the coordinates of the midpoint of each segment. 15. A( 5, 5), B(3, 5) ( 1, 0) 16. V(2, 6), W(4, 7) (3, 6.5) 17. C(6, 2), D(4, 7) (5, 4.5) 18. X(7, 8), Y( 7, 1) (0, 4.5) 19. E(7, 3), F( 1, 4) (3, 3.5) 20. A(5, 10), B( 4, 3) (0.5, 3.5) 21. G( 6, 2), H(2, 4) ( 2, 3) 22. C( 6, 7), D( 1, 1) ( 3.5, 3) 23. J(4, 1), K( 2, 2) (1, 0.5) 24. E( 4, 4), F (3, 5) ( 0.5, 4.5) 25. M(4, 8), N( 3, 4) (0.5, 6) 26. G(3, 1), H(5, 6) (4, 2.5) Glencoe/McGraw-Hill 515 Glencoe Pre-Algebra

37 9-6 Practice The Distance and Midpoint Formulas Find the distance between each pair of points. Round to the nearest tenth, if necessary. 1. A(5,2), B(3,4) C( 2, 4), D(1, 3) E( 3, 4), F( 2, 1) G(0, 0), H( 7, 8) R( 4, 8), S(2, 3) G(9, 9), H( 9, 9) M(1, 1), N( 10, 10) P(1 1 2, 3), Q(5, 6 1 ) R(7, ), S(6 1 2,3 1 4 ) T( 3 1 2, ), U(5 1 2,1 1 ) GEOMETRY Find the perimeter of each figure. 11. y y C 4 (5, 2) 8 O 2 A (3, 9) B (2, 8) F (8, 4) E (6, 6) O D (5, 1) The coordinates of the endpoints of a segment are given. Find the coordinates of the midpoint of each segment. 13. A(5, 1), B( 4, 3) (0.5, 1) 14. V(4, 6), W( 8, 12) ( 2, 3) 15. C( 2, 4), D( 5, 6) ( 3.5, 1) 16. X(1, 7), Y( 1, 7) (0, 0) 17. E(5, 3), F( 7, 8) ( 1, 2.5) 18. A(8, 8), B( 8, 8) (0, 0) 19. G(0, 6), H(12, 12) (6, 3) 20. C( 4, 6), D( 5, 14) ( 4.5, 4) 21. P( 7, 2), Q(8, 9) (0.5, 5.5) 22. J( 12, 3), K(4, 7) ( 4, 2) 23. Determine whether XYZ with vertices X(3, 4), Y(2, 3), and Z( 5, 2) is isosceles. Eplain your answer. Yes; X Y and Y Z equal 7.1 units. 24. Is DEF with vertices D(1, 4), E(6, 2), F ( 1, 3) a scalene triangle? Eplain. Yes; none of measures of the sides are equal. Glencoe/McGraw-Hill 516 Glencoe Pre-Algebra

38 9-6 Reading to Learn Mathematics The Distance and Midpoint Formulas Pre-Activity How is the Distance Formula related to the Pythagorean Theorem? Do the activity at the top of page 466 in your tetbook. Write your answers below. a. Name the coordinates of P. (3, 3) b. Find the distance between M and P. 7 units c. Find the distance between N and P. 3 units d. Classify MNP. right e. What theorem can be used to find the distance between M and N? Pythagorean Theorem f. Find the distance between M and N. 58 units Lesson 9-6 Reading the Lesson 1 3. See students work. Write a definition and give an eample of each new vocabulary word or phrase. Vocabulary Definition Eample 1. Distance Formula 2. midpoint 3. Midpoint Formula 4. The distance formula is based on the Pythagorean Theorem. 5. To determine the midpoint, you must know the coordinates of the endpoints of the line segment. Helping You Remember 6. Describe in a paragraph how you would find the perimeter of STU shown below. Write out any formulas that must be used. To find the perimeter of the triangle, you must use the Distance Formula (d ( 2 1 ) 2 (y 2 ) y 1 ) 2 to find the length of each side. Once you have the lengths of all three sides, add the lengths to find the perimeter. (1, 4) S U (4, 0) T (2, 2) Glencoe/McGraw-Hill 517 Glencoe Pre-Algebra

39 9-6 Enrichment Coordinate Proof Recall that the midpoint of a line segment is the point that separates the segment into two congruent segments. Use this justification of the -coordinate of the midpoint formula by beginning with RST. The midpoint is M(, y), and the distance between R and S is 2 units. Therefore, the distance between R and midpoint M is 1 unit. Write the reason for each statement. 1. Prove: ( 1 2 ) 2 Statement a b. 2( 1 ) 1( 2 1 ) c Reason O y M (, y) 1 R ( 1, y 1 ) a. Given (due to similar triangles) b. Cross Products c. Distributive Prop. 1 S ( 2, y 2 ) T ( 2, y 1 ) d e f g. 1 2 d. Add. Prop. Equality e. Simplify f. Comm. Prop. Add. g. Div. Prop. Equality Use Problem 1 as an eample to justify the y-coordinate of the midpoint. 2. Prove: y (y 1 y 2 ) 2 Statement a. 1 2 y y1 y y 2 b. 2(y y 1 ) 1 (y 2 y 1 ) c. 2y 2y 1 y 2 y 1 1 d. 2y 2y 1 2y 1 y 2 y 1 2y 1 e. 2y y 2 y 1 f. 2y y 1 y 2 g. y 2 y y 1 2 Reason a. Given (due to similar triangles) b. Cross Products c. Distributive Prop. d. Add. Prop. Equality e. Simplify f. Comm. Prop. Add. g. Div. Prop. Equality Glencoe/McGraw-Hill 518 Glencoe Pre-Algebra

40 9-7 Study Guide and Intervention Similar Triangles and Indirect Measurement Corresponding Parts of Similar Triangles Similar triangles are triangles that have the same shape but not necessarily the same size. If two triangles are similar, then the corresponding angles have the same measure, and the corresponding sides are proportional. Eample 1 AC B C D F EF The corresponding sides are proportional. Write a proportion Replace AC with 12, DF with 36, BC with 7, and EF with Find the cross products If ABC DEF, what is the value of? Simplify. 21 Divide each side by 12. D A B 12 m E 36 m 7 m C m F Lesson 9-7 Indirect Measurement The properties of similar triangles can be used to find measurements which are difficult to measure directly. This is called indirect measurement. Eample 2 The Chrysler Building in New York casts a foot shadow the same time a 5.8 foot tourist casts a 4.4 foot shadow. How tall is the Chrysler Building to the nearest tenth? Eercises tourist s height tourist s shadow Chrysler Building s height h Chrysler Building s shadow h 4.4 Find the cross products h Multiply h Divide each side by 4.4. The height of the Chrysler Building is 1046 feet. The triangles are similar. Write a proportion and find the value of Q 66 5 m A B 7 m C D E 10 m m 3. SURVEYOR A surveyor needs to find the distance AB across a pond. He constructs CDE similar to CAB and measures the distances as shown on this figure. Find AB yd F Glencoe/McGraw-Hill 519 Glencoe Pre-Algebra 17 m M N 22 m C O 51 m P 25 yd 60 yd D 12 yd E m R A yd B

41 9-7 Skills Practice Similar Triangles and Indirect Measurement In Eercises 1 10, the triangles are similar. Write a proportion to find each missing measure. Then find the value of A B 3 in. 4 in. C D E 6 in. in. F 2 m O 4 m X M 5 m N G 6 ft H 9 ft I J 8 ft K ft L Z m Y 4. R 12 m Q W 10 in S 14 cm m cm 15 m P U T 18 m U 21 cm V N 8 in. in. E O A 24 cm 16 in. B C F M D 7. G J H m 18 m I K 35 m 30 m L R M N 12 yd 15 yd yd 10 yd Q O 9. How far is the store from the bank? 10. How far is the tree from the flagpole? Gas 5 mi 8 mi 4 mi mi 10 yd yd Store 10 yd 20 yd $ Bank For Eercises 11 and 12, write a proportion. Then determine the missing measure. 11. ANIMALS At the same time a 12-foot adult elephant casts a 4.8-foot shadow, a baby elephant casts a 2-foot shadow. How tall is the baby elephant? 12 ft ft ; 5 ft 4. 8 ft 2 ft 12. AIRPORTS If a 12-meter-tall airplane hangar casts a 18-meter shadow at the same time a parked jet casts a 6-meter shadow, how tall is the jet? 12 1 m m ;4 meters 8 m 6 m Glencoe/McGraw-Hill 520 Glencoe Pre-Algebra

42 9-7 Practice Similar Triangles and Indirect Measurement In Eercises 1 10, the triangles are similar. Write a proportion to find each missing measure. Then find the value of. 1. C H km 36 B 4 m A 6 m D E 12 m m F 4. T 8 ft R 4 5. A G 15 U ft S 38 ft V 19 ft W 9 in. G B J Y 6 in. 10 in. I in. 3 in. K C X 32 in. 30 in. in. Z L O 9 km E Q M D 10 m m F H N 44 km 24 m 36 m I P km R Lesson yd 50.4 J 8 m L 7 m M 36 m yd K N 12 yd 15 yd For Eercises 9 12, write a proportion. Then determine the missing measure. 9. CHIMNEYS A 6-ft observer casts a 4-ft shadow at the same time the chimney on the Ohio Power Company casts an 804-foot shadow. How tall is the chimney? 6 ft ft ; 1206 ft 4 ft 8 04 ft 10. BUILDINGS The May Road Apartments in Hong Kong cast a 90-meter shadow at the same time a 1.5-meter tall tenant casts a 0.75-meter shadow. How tall is the apartment building? 1.5 m m 180 meters 0.75 m 9 0 m ; 11. WORLD RECORDS The world s tallest man lived from 1918 to He cast a 4-foot inch shadow when a 6-foot pole cast a 3-foot shadow. How tall was he? in. 7 2 in. ; 8 feet 11 inches 53.5 in. 36 in. 12. SHADOWS A man casts a 14-foot shadow. A 4-foot child casts a 9-foot 4-inch shadow at the same time. How tall is the man? in. 48 in. ; 6 feet 1 68 in in. Glencoe/McGraw-Hill 521 Glencoe Pre-Algebra

43 9-7 NAME DATE PERIOD Reading to Learn Mathematics Similar Triangles and Indirect Measurement Pre-Activity How can similar triangles be used to create patterns? Reading the Lesson Do the activity at the top of page 471 in your tetbook. Write your answers below. a. Compare the measures of the angles of each non-shaded triangle to the original triangle. They are the same. b. How do the lengths of the legs of the triangles compare? They are shorter See students work. Write a definition and give an eample of each new vocabulary word or phrase. Vocabulary Definition Eample 1. similar triangles 2. indirect measurement 3. The symbol means (is uneven, is similar to). 4. Indirect measurement uses the properties of (similar triangles, midpoints) to find measurements that are difficult to measure directly. Helping You Remember 5. Similar is a word that is used in everyday English. a. Find the definition of similar in a dictionary. Write the definition. related in appearance or nature; alike though not identical b. Eplain how the definition can help you remember how similar is used in mathematics. Similar triangles have angles that are the same and sides that, though not identical, are proportional. Glencoe/McGraw-Hill 522 Glencoe Pre-Algebra

44 9-7 Enrichment Constant Rate of Change rise In Chapter 8 you learned how to calculate the slope m of a line by using the ratio r un between any two points on the line. You may have wondered why it does not matter which two points you pick. Now that you have worked with similar triangles, it is possible to justify why all slopes on a line are the same. Points A, B, C, and D lie on the same line. We will show that the slope is the same when using points A and B as it is when using points C and D. y B C h 2 D v 2 F Lesson 9-7 A h 1 v 1 E O Write the reason for each statement. v 1. Prove: 1 v 2 h 1 h 2 Statement a. A E C F b. A C c. E F d. ABE CDF 1 e. v h v h 2 f. v 1 h 2 h 1 v g. v 1 h2 h h1 h2 h v h. 1 v 2 h 1 h v 2 h 2 Reason a. Definition of Horizontal Lines b. Corresponding s c. All Right s d. AA Similarity e. Def. Similar Triangles f. Cross Products g. Div. Prop. Equality h. Simplify Since r ise1 r ise2, any two points on a line can be used to calculate the slope. run run 1 2 Glencoe/McGraw-Hill 523 Glencoe Pre-Algebra

45 9-8 Study Guide and Intervention Sine, Cosine, and Tangent Ratios Trigonometric Ratios Words: If A is an acute angle of a right triangle, Symbols measure of leg opposite A sin A =, sin A = a measure of hypotenuse c cos A = b c tan A = a b measure of leg adjacent to A cos A =, Model measure of hypotenuse tan A = measure of leg opposite to A measure of leg adjacent to A B leg opposite a A hypotenuse c C b A leg adjacent to A Eample 1 sin D Find sin D, cos D, and tan D. measure of leg opposite D measure of hypotenuse F cos D Eample 2 Eercises 1 2 or measure of leg adjacent to D measure of hypotenuse tan D 5 or or Find each value to the nearest ten thousandth. a. cos 48 b. sin 32 COS 48 ENTER SIN 32 ENTER So, cos 48 is about So, sin 32 is about E 5 D measure of leg opposite to D measure of leg adjacent to D Find each sine, cosine, or tangent. Round to four decimal places, if necessary. 1. sin A sin D 0.28 B 3. cos A cos D tan C tan F Use a calculator to find each value to the nearest ten thousandth. 7. sin sin cos cos tan tan A 105 C D 96 E F 28 Glencoe/McGraw-Hill 524 Glencoe Pre-Algebra

46 9-8 Skills Practice Sine, Cosine, and Tangent Ratios Find each sine, cosine, or tangent. Round to four decimal places, if necessary. J 4 L E 36 F G 48 H D I K 1. sin D sin G sin K cos D cos G cos K tan D tan G tan K sin F sin I sin L cos F cos I cos L tan F tan I tan L 0.75 Use a calculator to find each value to the nearest ten thousandth. 19. sin tan cos cos sin tan tan cos sin sin tan cos cos sin tan Lesson 9-8 For each triangle, find each missing measure to the nearest tenth Glencoe/McGraw-Hill 525 Glencoe Pre-Algebra

47 9-8 Practice Similar Triangles and Indirect Measurement Find each sine, cosine, or tangent. Round to four decimal places, if necessary. B 40 A C 10 X 1. sin A sin X sin R cos A cos X cos R tan A tan X tan R sin C sin Z sin S cos C cos Z cos S tan C tan Z tan S 0.75 Use a calculator to find each value to the nearest ten thousandth. 19. sin tan cos cos sin tan sin tan cos For each triangle, find each missing measure to the nearest tenth. Y SHADOWS A tree casts a shadow 32 meters long when the angle of elevation of the sun is 37. How tall is the tree? about 24 m Z Q 9 R S Glencoe/McGraw-Hill 526 Glencoe Pre-Algebra

48 9-8 Reading to Learn Mathematics Sine, Cosine, and Tangent Ratios Pre-Activity How are ratios in right triangles used in the real world? Do the activity at the top of page 477 in your tetbook. Write your answers below. a. What type of triangle do the towrope, water, and height of the person above the water form? right b. Name the hypotenuse of the triangle. A C c. What type of angle do the towrope and the water form? acute d. Which side is opposite this angle? A B e. Other than the hypotenuse, name the side adjacent to this angle. B C Reading the Lesson 1 5. See students work. Write a definition and give an eample of each new vocabulary word or phrase. Vocabulary Definition Eample 1. trigonometry Lesson trigonometric ratio 3. sine 4. cosine 5. tangent Decide whether each statement is true or false. 6. Trigonometric ratios can be used with acute and obtuse angles. false 7. The value of the trigonometric ratio does not depend on the size of the triangle. true 8. To determine tangent, you must know the measure of the hypotenuse. false Helping You Remember 9. Develop a rhyme, abbreviation, or other memory device to help you remember the trigonometric ratios. Sample answer: SOH-CAH-TOA Glencoe/McGraw-Hill 527 Glencoe Pre-Algebra