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Chapter 8 Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such materials be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with the Glencoe Geometry program.

Any other reproduction, for sale or other use, is expressly prohibited.

Send all inquiries to:

Glencoe/McGraw-Hill

8787 Orion Place

Columbus, OH 43240 - 4027

ISBN: 978-0-07-890517-9

MHID: 0-07-890517-6

Printed in the United States of America.

4 5 6 7 8 9 10 11 12 REL 19 18 17 16 15 14 13 12 11

CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish.

ISBN10 ISBN13

Study Guide and Intervention Workbook 0-07-890848-5 978-0-07-890848-4 Homework Practice Workbook 0-07-890849-3 978-0-07-890849-1

Spanish Version

Homework Practice Workbook 0-07-890853-1 978-0-07-890853-8 ANSWERS FOR WORKBOOKS The answers for Chapter 8 of these workbooks can be found in the back of this Chapter Resource Masters booklet.

StudentWorks Plus

TM This CD-ROM includes the entire Student Edition text along with the English workbooks listed above.

TeacherWorks Plus

TM All of the materials found in this booklet are included for viewing, printing, and editing in this CD-ROM. Spanish Assessment Masters (ISBN10: 0-07-890856-6, ISBN13: 978-0-07-890856-9) These masters contain a Spanish version of Chapter 8 Test Form 2A and Form 2C. iii

Contents

Teacher"s Guide to Using the Chapter 8

Resource Masters .........................................iv

Chapter Resources

Chapter 8 Student-Built Glossary ......................1 Chapter 8 Anticipation Guide (English) .............3 Chapter 8 Anticipation Guide (Spanish) ............4

Lesson 8-1

Geometric Mean

Study Guide and Intervention ............................5 Skills Practice ....................................................7 Practice ..............................................................8 Word Problem Practice .....................................9 Enrichment ......................................................10

Lesson 8-2

The Pythagorean Theorem and

Its Converse

Study Guide and Intervention ..........................11 Skills Practice ..................................................13 Practice ..........................................................14 Word Problem Practice ...................................15 Enrichment ......................................................16 Spreadsheet Activity ........................................17

Lesson 8-3

Special Right Triangles

Study Guide and Intervention ..........................18 Skills Practice ..................................................20 Practice ..........................................................21 Word Problem Practice ...................................22 Enrichment ......................................................23

Lesson 8-4

Trigonometry

Study Guide and Intervention ..........................24 Skills Practice ..................................................26 Practice ..........................................................27 Word Problem Practice ...................................28

Enrichment ......................................................29Lesson 8-5Angles of Elevation and DepressionStudy Guide and Intervention ..........................30Skills Practice ..................................................32Practice ..........................................................33Word Problem Practice ...................................34Enrichment ......................................................35Lesson 8-6

The Law of Sines and Law of Cosines

Study Guide and Intervention ..........................36 Skills Practice ..................................................38 Practice ..........................................................39 Word Problem Practice ...................................40 Enrichment ......................................................41 Graphing Calculator Activity ............................42

Lesson 8-7

Vectors

Study Guide and Intervention ..........................43 Skills Practice ..................................................45 Practice ..........................................................46 Word Problem Practice ...................................47 Enrichment ......................................................48

Assessment

Student Recording Sheet ................................49 Rubric for Extended-Response .......................50 Chapter 8 Quizzes 1 and 2 .............................51 Chapter 8 Quizzes 3 and 4 .............................52 Chapter 8 Mid-Chapter Test ............................53 Chapter 8 Vocabulary Test .............................54 Chapter 8 Test, Form 1 ...................................55 Chapter 8 Test, Form 2A .................................57 Chapter 8 Test, Form 2B .................................59 Chapter 8 Test, Form 2C ................................61 Chapter 8 Test, Form 2D ................................63 Chapter 8 Test, Form 3 ...................................65 Chapter 8 Extended-Response Test ...............67 Standardized Test Practice .............................68 Answers ........................................... A1-A36 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. iv

Teacher"s Guide to Using the

Chapter 8 Resource Masters

The Chapter 8 Resource Masters includes the core materials needed for Chapter 8. These materials include worksheets, extensions, 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 on the

TeacherWorks Plus

TM CD-ROM.

Chapter Resources

Student-Built Glossary (pages 1-2) These

masters are a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. Give this to students before beginning Lesson 8-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson.

Anticipation Guide (pages 3-4) This

master, presented in both English and

Spanish, is a survey used before beginning

the chapter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their perceptions have changed.

Lesson Resources

Study Guide and Intervention These

masters provide vocabulary, key concepts, additional worked-out examples and

Check Your Progress exercises to use as a

reteaching activity. It can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.

Skills Practice This master focuses more

on the computational nature of the lesson.

Use as an additional practice option or as

homework for second-day teaching of the lesson.Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional practice option or as homework for second- day teaching of the lesson.

Word Problem Practice This master

includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson.

Enrichment These activities may extend

the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students" perspectives on the mathematics they are learning. They are written for use with all levels of students.

Graphing Calculator or Spreadsheet

Activities

These activities present ways in which

technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. v

Assessment Options

The assessment masters in the Chapter 8

Resource Masters offer a wide range of

assessment tools for formative (monitoring) assessment and summative (final) assessment.

Student Recording Sheet This master

corresponds with the standardized test practice at the end of the chapter.

Extended-Response Rubric This master

provides information for teachers and students on how to assess performance on open-ended questions.

Quizzes Four free-response quizzes offer

assessment at appropriate intervals in the chapter.

Mid-Chapter Test This 1-page test

provides an option to assess the first half of the chapter. It parallels the timing of the

Mid-Chapter Quiz in the Student Edition

and includes both multiple-choice and free- response questions.

Vocabulary Test This test is suitable for

all students. It includes a list of vocabulary words and 10 questions to assess students" knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests.Leveled Chapter Tests• Form 1 contains multiple-choice questions and is intended for use with below grade level students. • Forms 2A and 2B contain multiple-choice questions aimed at on grade level stu- dents. These tests are similar in format to offer comparable testing situations. • Forms 2C and 2D contain free- response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations. • Form 3 is a free-response test for use with above grade level students.

All of the above mentioned tests include a

free-response Bonus question.

Extended-Response Test Performance

assessment tasks are suitable for all students. Sample answers and a scoring rubric are included for evaluation.

Standardized Test Practice These three

pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and short- answer free-response questions.

Answers

• The answers for the Anticipation Guide and Lesson Resources are provided as reduced pages. • Full-size answer keys are provided for the assessment masters. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME DATE PERIOD

Chapter Resources

Chapter 8 1 Glencoe Geometry

Student-Built Glossary8

Vocabulary TermFound

on PageDefinition/Description/Example angle of depression angle of elevation component form cosine geometric mean

Law of Cosines

Law of Sines

magnitude (continued on the next page) This is an alphabetical list of the key vocabulary terms you will learn in Chapter 8. As you study the chapter, complete each term"s definition or description. Remember to add the page number where you found the term. Add these pages to your Geometry Study Notebook to review vocabulary at the end of the chapter. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME DATE PERIOD

Chapter 8 2 Glencoe Geometry

Student-Built Glossary (continued)8

Vocabulary TermFound

on PageDefinition/Description/Example

Pythagorean triple

resultant sine tangent trigonometric ratio trigonometry vector Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME DATE PERIOD

Chapter Resources

Chapter 8 3 Glencoe Geometry

Before you begin Chapter 8

• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).Anticipation GuideRight Triangles and Trigonometry

After you complete Chapter 8

• Reread each statement and complete the last column by entering an A or a D. • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.8Step 1

STEP 1

A, D, or NSStatementSTEP 2

A or D

1. The geometric mean between two numbers is the

positive square root of their product.

2. An altitude drawn from the right angle of a right

triangle to its hypotenuse separates the triangle into two congruent triangles.

3. In a right triangle, the length of the hypotenuse is

equal to the sum of the lengths of the legs.

4. If any triangle has sides with lengths 3, 4, and 5,

then that triangle is a right triangle.

5. If the two acute angles of a right triangle are 45°,

then the length of the hypotenuse is ⎷ ? 2 times the length of either leg.

6. In any triangle whose angle measures are 30°, 60°,

and 90°, the hypotenuse is ⎷ ? 3 times as long as the shorter leg.

7. The sine ratio of an angle of a right triangle is equal

to the length of the adjacent side divided by the length of the hypotenuse.

8. The tangent of an angle of a right triangle whose

sides have lengths 3, 4, and 5 will be smaller than the tangent of an angle of a right triangle whose sides have lengths 6, 8, and 10.

9. Trigonometric ratios can be used to solve problems

involving angles of elevation and angles of depression.

10. The Law of Sines can only be used in right triangles.

Step 2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NOMBRE FECHA PERÍODO

Antes de comenzar el Capítulo 8

• Lee cada enunciado. • Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado. • Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a).

PASO 1

A, D o NSEnunciadoPASO 2

A o D

1. La media geométrica de dos números es la raíz cuadrada

positiva de su producto.

2. Una altitud que se dibuja desde el ángulo recto de un

triángulo rectángulo hasta su hipotenusa divide el triángulo en dos triángulos congruentes.

3. En un triángulo rectángulo, la longitud de la hipotenusa

es igual a la suma de las longitudes de los catetos.

4. Si un triángulo rectángulo tiene lados con longitudes 3, 4 y

5, entonces cualquier triángulo es un triángulo

rectángulo.

5. Si los dos ángulos agudos de un triángulo rectángulo

son de 45°, entonces la longitud de la hipotenusa es ⎷ ? 2 veces la longitud de cualquiera de los catetos.

6. En cualquier triángulo cuyas medidas de ángulos sean

de 30°, 60° y 90°, la hipotenusa es ⎷ ? 3 veces tan larga como el cateto más corto.

7. La razón del seno para un ángulo en un triángulo

rectángulo es igual a la longitud del lado adyacente dividido entre la longitud de la hipotenusa.

8. La tangente para un ángulo de un triángulo rectángulo

cuyos lados tienen longitudes 3, 4 y 5 será menor que la tangente de un ángulo en un triángulo rectángulo cuyos lados tienen longitudes 6, 8 y 10.

9. Las razones trigonométricas se pueden usar para resolver

problemas de ángulos de elevación y ángulos de depresión.

10. La ley de los senos sólo se puede usar con triángulos

rectángulos.

Después de completar el Capítulo 8

• Vuelve a leer cada enunciado y completa la última columna con una A o una D. • ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?

• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los

enunciados que marcaste con una D.Ejercicios preparatoriosTriángulos rectángulos y trigonometría

Paso 1

Paso 2

8

Capítulo 8 4 Geometría de Glencoe

Lesson 8-1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME DATE PERIOD

Chapter 8 5 Glencoe Geometry

Study Guide and Intervention

Geometric Mean

Geometric Mean The geometric mean between two numbers is the positive square root of their product. For two positive numbers a and b, the geometric mean of a and b is the positive number x in the proportion a ? x = x ? b . Cross multiplying gives x2 = ab, so x = ⎷ ?? ab . Find the geometric mean between each pair of numbers. a. 12 and 3 x = ⎷ ?? ab Definition of geometric mean ⎷ ??? 12 . 3 a = 12 and b = 3 ⎷ ????? (2 . 2 . 3) . 3 Factor. = 6 Simplify. The geometric mean between 12 and 3 is 6.b. 8 and 4 x = ⎷ ?? ab Definition of geometric mean ⎷ ?? 8 . 4 a = 8 and b = 4 ⎷ ???? (2 . 4) . 4 Factor. ⎷ ??? 16 . 2 Associative Property = 4 ⎷ ? 2 Simplify.

The geometric mean between 8 and 4

is 4 ⎷ ? 2 or about 5.7.

Exercises

Find the geometric mean between each pair of numbers.

1. 4 and 4 2. 4 and 6

3. 6 and 9 4. 1

? 2 and 2

5. 12 and 20 6. 4 and 25

7. 16 and 30 8. 10 and 100

9. 1 ? 2 and 1 ? 4 10. 17 and 3

11. 4 and 16 12. 3 and 24 8-1

Example

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