Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Photo Credits Cover Jupiter Images; iv (tl bl br) File Photo, (tc tr) The McGraw-Hill Companies, (cl c) Doug Martin, (cr) Aaron Haupt; v (1 11 12) The McGraw-Hill Companies, (5 10 13 14) File Photo; viii CORBIS; viii Mitchell Funk/Getty Images; ix S Alden/PhotoLink/Getty Images; xi Peter Barritt/Alamy; 2–3 Mike Brinson/Getty Images; (Frame) Getty Images; (inset) Ryan McVay/Getty Images; 15 Comstock/CORBIS; 16 CORBIS; 25 Jerry Irwin/Photo Researchers, Inc.; 34 42 CORBIS; 52 Getty Images; 53 CORBIS; 061 Ingram Publishing/ SuperStock; 068 (b) CORBIS, (t) Rudi Von Briel/PhotoEdit; 70 71 CORBIS; 77 Getty Images; 78 CORBIS; 79 Comstock/Imagestate; 80 CORBIS; 95 Punchstock Copyright © 2008 by The McGraw-Hill Companies, Inc All rights reserved Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-07-878214 MHID: 0-07-878214-7 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 6B California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction 1B Chapter Multiplication 1B Chapter Division 1B Chapter Integers Volume Fractions and Decimals 2A Chapter Parts of a Whole 2A Chapter Equivalence of Fractions 2B Chapter Operations with Fractions 2B Chapter Positive and Negative Fractions and Decimals Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Volume Ratios, Rates, and Percents 3A Chapter Ratios and Rates 3A Chapter Percents, Fractions, and Decimals 3B Chapter Using Percents 3B Chapter Rates and Proportional Reasoning Volume The Core Processes of Mathematics 4A Chapter Operations and Equality 4A Chapter Math Fundamentals 4B Chapter Math Expressions 4B Chapter Linear Equations 4B Chapter Inequalities Volume Functions and Equations 5A Chapter Patterns and Relationships 5A Chapter Graphing 5B Chapter Proportional Relationships 5B Chapter The Relationship Between Graphs and Functions Volume Measurement 6A Chapter How Measurements Are Made 6A Chapter Length and Area in the Real World 6B Chapter Exact Measures in Geometry 6B Chapter Angles and Circles iii Authors and Consultants AUTHORS Frances Basich Whitney Kathleen M Brown Dixie Dawson Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Math Curriculum Leader Long Beach Unified Long Beach, California Philip Gonsalves Robyn Silbey Kathy Vielhaber Mathematics Coordinator Alameda County Office of Education Hayward, California Math Specialist Montgomery County Public Schools Gaithersburg, Maryland Mathematics Consultant St Louis, Missouri Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California Dinah Zike Educational Consultant, Dinah-Might Activities, Inc San Antonio, Texas CONSULTANTS Assessment Donna M Kopenski, Ed.D Math Coordinator K–5 City Heights Educational Collaborative San Diego, California iv Instructional Planning and Support ELL Support and Vocabulary Beatrice Luchin ReLeah Cossett Lent Mathematics Consultant League City, Texas Author/Educational Consultant Alford, Florida Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc CONTRIBUTING AUTHORS California Advisory Board CALIFORNIA ADVISORY BOARD Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Glencoe wishes to thank the following professionals for their invaluable feedback during the development of the program They reviewed the table of contents, the prototype of the Student Study Guide, the prototype of the Teacher Wraparound Edition, and the professional development plan Linda Anderson Cheryl L Avalos Bonnie Awes Kathleen M Brown 4th/5th Grade Teacher Oliveira Elementary School, Fremont, California Mathematics Consultant Retired Teacher Hacienda Heights, California Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Carol Cronk Audrey M Day Jill Fetters Grant A Fraser, Ph.D Mathematics Program Specialist San Bernardino City Unified School District San Bernardino, California Classroom Teacher Rosa Parks Elementary School San Diego, California Math Teacher Tevis Jr High School Bakersfield, California Professor of Mathematics California State University, Los Angeles Los Angeles, California Eric Kimmel Donna M Kopenski, Ed.D Michael A Pease Chuck Podhorsky, Ph.D Mathematics Department Chair Frontier High School Bakersfield, California Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Math Coach Aspire Public Schools Oakland, California Math Director City Heights Educational Collaborative San Diego, California Arthur K Wayman, Ph.D Frances Basich Whitney Mario Borrayo Melissa Bray Professor Emeritus California State University, Long Beach Long Beach, California Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, CA Teacher Rosa Parks Elementary San Diego, California K–8 Math Resource Teacher Modesto City Schools Modesto, California v California Reviewers CALIFORNIA REVIEWERS Each California Reviewer reviewed at least two chapters of the Student Study Guides, providing feedback and suggestions for improving the effectiveness of the mathematics instruction Melody McGuire Math Teacher California College Preparatory Academy Oakland, California 6th and 7th Grade Math Teacher McKinleyville Middle School McKinleyville, California Eppie Leamy Chung Monica S Patterson Teacher Modesto City Schools Modesto, California Educator Aspire Public Schools Modesto, California Judy Descoteaux Rechelle Pearlman Mathematics Teacher Thornton Junior High School Fremont, California 4th Grade Teacher Wanda Hirsch Elementary School Tracy, California Paul J Fogarty Armida Picon Mathematics Lead Aspire Public Schools Modesto, California 5th Grade Teacher Mineral King School Visalia, California Lisa Majarian Anthony J Solina Classroom Teacher Cottonwood Creek Elementary Visalia, California Lead Educator Aspire Public Schools Stockton, California vi Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Bobbi Anne Barnowsky Volume 6A Measurement Chapter How Measurements Are Made 1-1 Unit Conversions: Metric Length 3AF1.4, 3MG1.4, 6AF2.1 1-2 Unit Conversions: Customary Length 11 3AF1.4, 3MG1.4, 6AF2.1 Progress Check .18 1-3 Unit Conversions: Metric Capacity and Mass 19 3AF1.4, 3MG1.4, 6AF2.1, 7MG1.1 1-4 Unit Conversions: Customary Capacity and Weight… 25 3AF1.4, 3MG1.4, 6AF2.1 Progress Check .32 1-5 Time and Temperature 33 3AF1.4, 3MG1.4, 6AF2.1, 7MG1.1 1-6 Analyze Units of Measure .39 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc 6AF2.1, 7MG1.1, 7MG1.3 Progress Check .46 Assessment Study Guide .47 Chapters and are contained in Volume 6A Chapters and are contained in Volume 6B Standards Addressed in This Chapter 3AF1.4 Express simple unit conversions in symbolic form (e.g., _ inches = _ feet × 12) 3MG1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes) 6AF2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches) 7MG1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters) 7MG1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer Chapter Test .50 Standards Practice 52 Lake Tahoe vii Contents Chapter Length and Area in the Real World Standards Addressed in This Chapter 2-1 Length 56 2MG1.3, 4MG2.2, 4MG2.3 2-2 Perimeter 63 3MG1.3 Progress Check .70 2-3 Introduction to Area .71 3MG1.2 2-4 Introduction to Volume 77 3MG1.2 Progress Check .83 Assessment 2MG1.3 Measure the length of an object to the nearest inch and/or centimeter 3MG1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them 3MG1.3 Find the perimeter of a polygon with integer sides 4MG2.2 Understand that the length of a horizontal line segment equals the difference of the x-coordinates 4MG2.3 Understand that the length of a vertical line segment equals the difference of the y-coordinates Study Guide .84 Chapter Test .88 Standards Practice 90 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc viii Alamo Square, San Francisco Contents Chapter Exact Measures in Geometry 3-1 Area of a Rectangle 3MG1.2, 4MG1.1 3-2 Area of a Parallelogram 11 4MG1.1, 5MG1.1 Progress Check .18 3-3 Area of a Triangle 19 3MG1.2, 5MG1.1 3-4 Surface Area of Rectangular Solids 27 3MG1.2, 4MG1.1, 5MG1.2 Progress Check .36 3-5 Volume of Rectangular Solids .37 3MG1.2, 5MG1.3 Assessment Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Study Guide .43 Chapter Test .48 Standards Practice 50 Santa Cruz Chapters and are contained in Volume 6A Chapters and are contained in Volume 6B Standards Addressed in This Chapter 3MG1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them 4MG1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square kilometer (km2), square inch (in.2), square yard (yd.2), or square mile (mi.2) 5MG1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing each with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by pasting and cutting a right triangle on the parallelogram) 5MG1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to complete the surface area for these objects 5MG1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm3], cubic meter [m3], cubic inch [in.3], cubic yard [yd.3]) to compute the volume of rectangular solids ix Contents Chapter Angles and Circles Standards Addressed in This Chapter 4-1 Lines 5MG2.1 54 4-2 Angles 5MG2.1 63 Progress Check 72 4-3 Triangles and Quadrilaterals 5MG2.1 73 4-4 Add Angles 5MG2.1, 5MG2.2, 6MG2.2 81 Progress Check 90 4-5 Congruent Figures 7MG3.4 91 4-6 Pythagorean Theorem 5MG2.1, 7MG3.3 99 Progress Check 108 4-7 Circles 6MG1.2 .109 4-8 Volume of Triangular Prisms and Cylinders 117 6MG1.3 Progress Check 127 Study Guide 128 Chapter Test 134 Standards Practice .136 Mono Lake Tufa State Reserve 5MG2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems 6MG1.2 Know common estimates 22 of π (3.14, _) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements 6MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid 6MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle 7MG3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement 7MG3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationship between the sides and angles of the two figures x Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Assessment 5MG2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straight edge, ruler, compass, protractor, drawing software) Guided Practice Name each solid figure cylinder triangular prism Step by Step Practice JO Find the volume of the solid figure whose base is an isosceles triangle Step Find the length of the base and height of the triangle of Use the Pythagorean Theorem to find the height the triangle JO Copyright © by The McGraw-Hill Companies, Inc The base of the triangular prism is an isosceles triangle The length of the base of the isosceles triangle is inches Therefore, the length of half the base is ÷ = inches for a and for c in the Substitute for Pythagorean Theorem a2 + b2 = c2 + b2 = + b2 = 25 b2 = 16 b= Remember that the Pythagorean Theorem states that in a right triangle a2 + b2 = c2 JO JO JO JO JO Step Find the area of the base of the triangular prism Use the formula for the area of a triangle The length of the base of the triangle is and the height of the triangle is JO inches, inches Step Substitute the area of the base and the height into the formula for the volume Then multiply The volume of the triangular prism is 144 cubic inches bh A = 1× A = A= × 12 V=B×h V = 12 × V = 144 12 GO ON Lesson 4-8 Volume of Triangular Prisms and Cylinders 121 Find the volume of each solid figure Use 3.14 for π The diameter of the circle is 20 centimeters, so the radius is 20 ÷ = 10 Use 3.14 for π A = πr2 A ≈ 3.14 × A ≈ 314 10 DN DN Substitute the area of the base and the height into the formula for the volume Then multiply V=B×h V ≈ 314 × V ≈ 1,570 The volume of the cylinder is about 1,570 cubic centimeters The length of the base of the triangle is of the triangle is yards bh A = A=1× A= yards and the height ZE × ZE ZE Substitute the area of the base and the height into the volume formula Then multiply 13 The volume of the triangular prism is 117 cubic yards DN N DN N N The volume of the triangular prism is cubic meters 122 Chapter Angles and Circles The volume of the cylinder is about 141,300 cubic centimeters Copyright © by The McGraw-Hill Companies, Inc V=B×h V= × V = 117 Step by Step Problem-Solving Practice Problem-Solving Strategies Solve CONTAINERS Marta has a cylinder-shaped container The diameter of the base is 14 centimeters, and the height is 25 centimeters What is the volume of the container? Understand Draw a diagram Look for a pattern Act it out ✓ Use a formula Work backward Read the problem Write what you know The diameter of the base of the container is 14 centimeters The height of the container is 25 centimeters Pick a strategy One strategy is to use a formula Plan Think of the problem as two parts Use a formula to find the area of the circular base Then use a formula to find the volume Use 3.14 for π The diameter of the circle is 14 radius is 14 ÷ = Solve centimeters, so the DN DN Copyright © by The McGraw-Hill Companies, Inc A = πr A ≈ 3.14 × A ≈ 153.86 Substitute the area of the base and the height into the formula for the volume Then multiply V=B×h 25 V ≈ 153.86 × V ≈ 3,846.5 The volume of the container is about 3,846.5 cubic centimeters Use a calculator to check your answer Check CANDLES Conrad’s Candle Shop has two dozen candles shaped like triangular prisms The largest candle has a height of inches and a triangular base The length of the triangular base is inches, and its height is inches What is the volume of the candle? 105 in3 Check off each step ✔ Understand ✔ Solve ✔ Plan ✔ Check GO ON Lesson 4-8 Volume of Triangular Prisms and Cylinders 123 10 JO SCIENCE The cylindrical beakers in Mr Peters’s biology class have a diameter of inches and a height of 10 inches What is the volume of each beaker? Use 3.14 for π 196.25 in3 JO A box of crackers is in the shape of a rectangular prism Use what you know about finding the volume of a triangular prism to find the volume of the box 11 Find the area of the base of the rectangular prism The area of a rectangle is A = l × w = × = 12 JO square inches Multiply the area of the base by the height of the prism: 12 × = 72 cubic inches JO JO JO JO Skills, Concepts, and Problem Solving Name each solid figure 12 13 triangular prism Find the volume of each solid figure Use 3.14 for π 14 15 GU JO GU GU JO The volume of the triangular prism 45 is cubic feet 124 Chapter Angles and Circles The volume of the cylinder is about 3,416.32 cubic inches Copyright © by The McGraw-Hill Companies, Inc cylinder Solve 16 CONSTRUCTION To keep the wind from blowing his door shut, Lorenzo made a doorstop The doorstop is shaped like a triangular prism The base triangle has a length of centimeters and a height of 15 centimeters The height of the prism is centimeters What is the volume of Lorenzo’s doorstop? 360 cm 17 FOOD Belinda’s mother stores bagels in a cylinder-shaped container to keep them fresh The diameter of the container is inches, and its height is 11 inches What is the volume of the container? Use 3.14 for π 310.86 in Vocabulary Check Write the vocabulary word that completes each sentence 18 19 Copyright © by The McGraw-Hill Companies, Inc 20 21 A(n) triangular prism is a prism whose bases are triangular with parallelograms for sides Volume is the number of cubic units needed to fill a three-dimensional figure or solid figure cylinder A(n) is a three-dimensional figure having two parallel congruent circular bases and a curved surface connecting the two bases Writing in Math Explain how to find the volume of a triangular prism Find the area of the base using the formula for the area of a triangle Substitute the area of the base and height into the formula for the volume Then multiply Spiral Review 22 SPORTS The radius of Phoebe’s circular-shaped swimming pool is 5.5 feet She swam across the pool times How many feet did Phoebe swim? (Lesson 4-7, p 109) 44 feet GO ON Lesson 4-8 Volume of Triangular Prisms and Cylinders 125 Are the figures congruent? 23 (Lesson 4-5, p 91) ¡ ¡ ¡ ¡ - ¡ ¡ / congruent LMN and VWX are because corresponding sides and corresponding angles are congruent Draw a figure with the description given 24 right, isosceles triangle 5×3×4 " # % 126 Chapter Angles and Circles $ (Lesson 3-4, p 27) Copyright © by The McGraw-Hill Companies, Inc Draw a net for the dimensions given ! trapezoid 25 26 (Lesson 4-3, p 73) Chapter Progress Check (Lessons 4-7 and 4-8) Identify the length of the radius and diameter of each circle 6MG1.2 3.5 radius: diameter: in 2.75 cm radius: 5.5 diameter: cm in DN JO Find the circumference and area of the circle Use 3.14 for π 6MG1.2 The circumference of the circle is about 56.52 yards, and the area of the circle is about 254.34 square yards ZE _ Find the circumference and area of the circle Use 22 for π 6MG1.2 The circumference of the circle is about The area of the circle is about 44 or 6_ _ 7 44 or 6_ _ 7 feet square feet GU Find the volume of each solid figure Use 3.14 for π 5MG1.3, 6MG1.3 Copyright © by The McGraw-Hill Companies, Inc JO N N JO N The volume of the triangular prism 75 is cubic meters The volume of the cylinder is about 4,615.8 cubic inches Solve 5MG1.3, 6MG1.3, 6MG1.2 FOOD Kizzie purchased a triangular wedge of cheddar cheese The cheese had a triangle base with length centimeters and height 12 centimeters The height of the cheese wedge was centimeters What was the volume of the wedge of cheese? 378 cm BASEBALL According to baseball regulations, the pitcher’s mound, which is circular, must have a diameter of 18 feet What is the area of a pitcher’s mound? 254.34 ft Lesson 4-8 Volume of Triangular Prisms and Cylinders 127 Chapter Study Guide Vocabulary and Concept Check cylinder, p 117 Write the vocabulary word that completes each sentence degree, p 63 A(n) protractor is an instrument marked in degrees, used for measuring or drawing angles A(n) degree angles A(n) diameter is a chord that passes through the center of a circle diameter, p 109 hypotenuse, p 99 parallel lines, p 54 pi (π), p 109 protractor, p 63 Pythagorean Theorem, p 99 radius, p 109 trapezoid, p 73 triangular prism, p 117 is a unit for measuring The Pythagorean Theorem states that the sum of the squares of the lengths of the legs in a right triangle is equal to the square of the length of the hypotenuse Pi (π) is the ratio of the circumference of a circle to the diameter of the same circle Its value is 22 approximately 3.14 or _ Label each diagram below Write the correct vocabulary term in each blank parallel lines radius cylinder trapezoid 10 hypotenuse 11 triangular prism 128 Chapter Study Guide Copyright © by The McGraw-Hill Companies, Inc Lesson Review 4-1 Lines Example (pp 54–62) Name each line Identify the relationships Name each line Identify the relationships : 12 " # : ; perpendicular The lines are lines PQ ⊥ 13 & ' - parallel The lines are lines EF 4-2 YZ Angles (pp 63–71) ; 105° ∠XYZ measures ∠XYZ is a(n) obtuse angle Example Measure and identify the angle Place the center of the protractor at point B Line up BC with the line that extends from 0° to 180° on the protractor 15 # # 35° ∠MNP measures acute ∠MNP is a(n) angle " $ / " Copyright © by The McGraw-Hill Companies, Inc : AB intersects XY LM Measure and identify the angle 14 One line is AB The other line is XY The lines cross, or intersect The lines not form right angles, so they are not perpendicular lines The lines are intersecting lines $ Look at point C Read the measure of the angle where BA passes through the inner scale ∠ABC measures 45° Chapter Study Guide 129 4-3 Triangles and Quadrilaterals (pp 73–80) Identify each figure Example 16 Identify the figure The figure is a(n) trapezoid 17 The figure has three sides and three angles The figure is a triangle None of its sides are equal in length The figure is a scalene triangle The figure is a(n) acute, isosceles triangle 4-4 Add Angles One angle is an obtuse angle The figure is an obtuse, scalene triangle (pp 81–89) What types of angles are shown? Example ( 18 % What is the measure of the missing angle? ¡ ¡ & ' ' ¡ & ¡ Find the measure of each missing angle 19 ¡ Find the sum of the measures of known angles : ¡ ¡ ¡ m∠Q + m∠R + m∠S = 300° ¡ ¡ ; The measure of the missing angle is 145° # 20 ¡ " ¡ ¡ $ The measure of the missing angle is 30° 130 The sum of the measures of the angles of a quadrilateral is 360° Subtract the sum of the known measures from 360° 360° - 300° = 60° Chapter Study Guide Copyright © by The McGraw-Hill Companies, Inc See TWE margin Sketch complementary angles when one angle’s measure is 80° Example Sketch supplementary angles when one angle’s measure is 50° 21 ¡ ¡ ¡ ¡ The sum of supplementary angles equals 180° Using your protractor, sketch a 180° angle Find the given angle, 50°, inside the 180° angle and make a dot Use a straightedge to draw the ray that connects the vertex and the dot at 50° Find the missing angle by using the protractor’s scale The supplementary angle is 130° Copyright © by The McGraw-Hill Companies, Inc 4-5 22 Congruent Figures (pp 91–98) Example Are the triangles congruent? Are the quadrilaterals congruent? - / ¡ ¡ ¡ - ¡ ¡ ¡ ¡ ¡ ¡ ¡ Corresponding angles are congruent and corresponding sides are congruent Therefore, the two triangles are congruent ¡ ¡ ¡ Are corresponding angles congruent? m∠S m∠J m∠T m∠K m∠U m∠L m∠V m∠M , ¡ + Are corresponding sides congruent? −− −− ST JK −− −− TU KL −−− −−− UV LM −− −− SV JM Quadrilaterals STUV and JKLM are congruent because all of the corresponding angles and sides are congruent Chapter Study Guide 131 4-6 23 Pythagorean Theorem Find the length of the leg of the right triangle (pp 99–107) Example B Find the length of the leg of the right triangle From the figure, you know a = 15 and c = 25 The length of the leg is 24 units Find the length of the hypotenuse of the right triangle 4-7 25 Circles units What is the area of the circle? 22 for π Use _ 22 A ≈ _ × 42 What is the area of the circle? JO What is the area of the circle? 22 for π Use _ 22 A ≈ _ × 62 22 × 36 A ≈ _ 132 Chapter Study Guide GU The radius is cm; r = 22 Substitute for r and _ for π in the area formula DN A = πr2 22 × 72 A ≈ _ 22 A ≈ _ × 49 A ≈ 22 × A ≈ 154 The area of the circle is about 154 cm2 Copyright © by The McGraw-Hill Companies, Inc 352 in _ A≈ 792 ft _ The length of the leg is 20 units Example A≈ C (pp 109–116) 22 × 16 A ≈ _ 26 Substitute the values of a and c in the Pythagorean Theorem and solve for b a2 + b2 = c2 152 + b2 = 252 225 + b2 = 625 b2 = 400 b = 20 D The length of the leg is 4-8 27 Volume of Triangular Prisms and Cylinders (pp 117–126) What is the volume of the triangular prism whose base is a right triangle? JO JO JO The volume of the triangular prism is 420 in 28 What is the volume of the triangular prism? DN DN DN The volume of the triangular prism is about 600 cm Copyright © by The McGraw-Hill Companies, Inc 29 Example What is the volume of the triangular prism whose base is a right triangle? The length of the base of the triangle is cm, and the height of the triangle is cm DN DN DN Use the area-of-atriangle formula to find the area of the base bh A = 1×6×4 A = A = 12 Substitute the area of the base and the height into the volume formula Then multiply V=B×h V = 12 × 10 V = 120 The volume of the triangular prism is 120 cm3 What is the volume of the cylinder? JO Example 10 What is the volume of the cylinder? JO The volume of the cylinder is about 141.3 in3 30 What is the volume of the cylinder? DN The radius of the circle is ft Use the formula for the area of a circle to find the area of the base Use 3.14 for π GU GU A = πr2 A ≈ 3.14 × 12 A ≈ 3.14 Substitute the area of the base and for the height into the volume formula Then multiply DN The volume of the cylinder is about 942 cm3 V=B×h V ≈ 3.14 × V ≈ 9.42 The volume of the cylinder is about 9.42 ft3 Chapter Study Guide 133 Chapter Chapter Test Draw each figure 5MG2.1 perpendicular lines OP and XY : - 5MG2.1 Measure and identify the angle 5MG2.1 " # The lines are LM parallel QR 5MG2.1 rhombus ¡ $ 75 ∠ABC measures acute angle ∠ABC is a(n) lines Draw a figure with the description given 5 Name each line Identify the relationships line segment ST ° Draw each type of angle given 5MG 2.1, 5GM2.2 complementary angles Find the measure of the missing angle 5MG2.2, 6MG2.2 , Are the figures congruent? 7MG3.4 ¡ ¡ + ¡ ( ¡ - The measure of the missing angle 51 is ° ¡ ¡ ¡ STU and ) ¡ ¡ ' FGH are congruent because corresponding sides and corresponding congruent angles are GO ON 134 Chapter Test Copyright © by The McGraw-Hill Companies, Inc Find the length of the hypotenuse of the right triangle 7MG3.3 The length of the hypotenuse is 15 D units Use the circle for Exercises 10–13 Use 3.14 for π 6MG1.2 50 m 10 diameter = 11 radius = 12 circumference ≈ 13 area ≈ 14 N Find the volume Use 3.14 for π The volume of the cylinder is about 231.732 ft 6MG1.3 GU 25 m GU 157 m 1,962.50 m Solve 5MG2.1, 7MG3.4, 6MG1.3 15 CONSTRUCTION Marcel had to fit two pieces of crown molding together at a 90° angle What type of angle did the molding form? Copyright © by The McGraw-Hill Companies, Inc right 16 COOKING Annie made some fried corn tortillas like the one pictured at the right What type of triangle Annie’s tortillas equilateral triangles represent? 17 SHAPES Miss Rustin is making a collage for her club The two shapes she is using are shown at the right Are these shapes congruent? T JODIFT No, they are not congruent 18 FOOD The soup kitchen uses cans of soup that have a diameter of inches and a height of inches What is the volume of a cylindrical soup can? Use 3.14 for π about 301.44 in3 Correct the mistakes 7MG3.3 19 When Aida took her geometry test, this was how she answered the following question: Mr Hauser has a ladder resting against his bedroom wall The top of the ladder touches the wall at a height of 12 feet The ladder is 15 feet in length How far is the bottom of Mr Hauser’s ladder from the base of his bedroom wall? n 5HEDISTANCE OFTHELADDER FROMTHEBASE OFTHEWALLIS FT See TWE margin Chapter Test 135 ... United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 6B California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A... Elementary School, Fremont, California Mathematics Consultant Retired Teacher Hacienda Heights, California Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California Math Curriculum Staff... Elementary School San Diego, California Math Teacher Tevis Jr High School Bakersfield, California Professor of Mathematics California State University, Los Angeles Los Angeles, California Eric Kimmel