Lesson 6.1 Skills Practice

Similar documents
Whirlygigs for Sale! Rotating Two-Dimensional Figures through Space. LESSON 4.1 Skills Practice. Vocabulary. Problem Set

Catty Corner. Side Lengths in Two and. Three Dimensions

Pythagorean Theorem. 2.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem... 45

6.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem Can That Be Right? 6.3 Pythagoras to the Rescue

Students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions.

The Pythagorean Theorem 8.6.C

Student Instruction Sheet: Unit 4 Lesson 1. Pythagorean Theorem

Square Roots and the Pythagorean Theorem

Squares and Square Roots Algebra 11.1

UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet

ACCELERATED MATHEMATICS CHAPTER 14 PYTHAGOREAN THEOREM TOPICS COVERED: Simplifying Radicals Pythagorean Theorem Distance formula

1. Convert 60 mi per hour into km per sec. 2. Convert 3000 square inches into square yards.

Essential Mathematics Practice Problems for Exam 5 Chapter 8

Grade 8 The Pythagorean Theorem

Read each question carefully and fill in the bubble with the letter of the correct answer or answers on your answer sheet.

3.9. Pythagorean Theorem Stop the Presses. My Notes ACTIVITY

The Pythagorean Theorem is used in many careers on a regular basis. Construction

The Pythagorean Theorem

Fair Game Review. Chapter 4. Name Date. Find the area of the square or rectangle Find the area of the patio.

G.MG.A.3: Area of Polygons

You may use a calculator. Answer the following questions. (5 pts; partial credit at teacher discretion)

Length and area Block 1 Student Activity Sheet

11.2 Areas of Trapezoids,

The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2.

Grade 8. The Pythagorean Theorem 8.G COMMON CORE STATE STANDARDS ALIGNED MODULES

Geometry. Practice Pack

Name Date. Chapter 15 Final Review

GA Benchmark 8th Math (2008GABench8thMathset1)

Area of Composite Figures. ESSENTIAL QUESTION How do you find the area of composite figures? 7.G.2.6

Lesson: Pythagorean Theorem Lesson Topic: Use Pythagorean theorem to calculate the hypotenuse

SIXTH GRADE MATHEMATICS CHAPTER 10 AREA AND PERIMETER TOPICS COVERED:

Lesson 1 Area of Parallelograms

Geometry 2001 part 1

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 17, :30 to 3:30 p.m.

Area of Composite Figures. ESSENTIAL QUESTION do you find the area of composite figures? 7.9.C

Unit 1, Lesson 1: What are Scaled Copies?

th Grade Test. A. 128 m B. 16π m C. 128π m

AREA See the Math Notes box in Lesson for more information about area.

Geometry. Warm Ups. Chapter 11

UNIT 10 PERIMETER AND AREA

h r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck.

Unit 5 and 6 Exam (Modules 11 through 15)

Part I Multiple Choice

June 2016 Regents GEOMETRY COMMON CORE

Name Period No. Geometry Unit Review with Application Problems

All About That Base... and Height

The Grade 6 Common Core State Standards for Geometry specify that students should

MATH MEASUREMENT AND GEOMETRY

3 Kevin s work for deriving the equation of a circle is shown below.

Pythagorean Theorem. If Z = 15 cm and X = 17 cm, what is the length of Y? Write your response here: (show your work)

Page 1 part 1 PART 2

Name Date MASCOT PAINTING. Use the picture on the left and enlarge it by using the grid below. II Classroom Strategies Blackline Master

TERRA Environmental Research Institute

Geometry Topic 4 Quadrilaterals and Coordinate Proof

Write an equation that can be used to answer the question. Then solve. Round to the nearest tenth if necessary. 1. How far up the tree is the cat?

1. A maintenance technician sights the top of a telephone pole at a 25 angle of elevation as shown.

WVDE Math 7 G Solve Real-life and Mathematical Problems involving Angle Measure, Area, Surface Area, and Volume Test

#2. Rhombus ABCD has an area of 464 square units. If DB = 18 units, find AC. #3. What is the area of the shaded sector if the measure of <ABC is 80?

Use a calculator to find the volume of a sphere when the radius is 6. (V = 4 3 πr 3 )

Geometry Final Exam Review 2012 #

How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr.

8-1 L E S S O N M A S T E R. Name

5-8 Scale Drawings and Models

Set 6: Understanding the Pythagorean Theorem Instruction

Representing Square Numbers. Use materials to represent square numbers. A. Calculate the number of counters in this square array.

KCATM Geometry

Foundations of Math 11: Unit 2 Proportions. The scale factor can be written as a ratio, fraction, decimal, or percentage

3.3. You wouldn t think that grasshoppers could be dangerous. But they can damage

Assignment Assignment for Lesson 3.1

Grade 8 Math Fourth Six Weeks Three Week Test

Ch 11 Pre-HS Area SOLs 50 Points Name:

Pythagorean Theorem Unit

2016 Summer Break Packet for Students Entering Geometry Common Core

Grade 7, Unit 1 Practice Problems - Open Up Resources

FSA Geometry EOC Getting ready for. Circles, Geometric Measurement, and Geometric Properties with Equations.

Concept: Pythagorean Theorem Name:

Lesson 3 Pre-Visit Perimeter and Area

Similar Figures 2.5. ACTIVITY: Reducing Photographs. How can you use proportions to help make decisions in art, design, and magazine layouts?

6.00 Trigonometry Geometry/Circles Basics for the ACT. Name Period Date

Math Review Questions

GEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1)

16. DOK 1, I will succeed." In this conditional statement, the underlined portion is

Geometry: Measuring Two-Dimensional Figures

Droodle for Geometry Final Exam

Lesson 8.3: Scale Diagrams, page 479

Area and Perimeter. Practice 1 Area of a Rectangle. Find the area of each figure. Example. one-inch squares.

Chapter 8 Practice Test

5/6 Lesson: Angles, measurement, right triangle trig, and Pythagorean theorem

Squares and Square Roots

18 Two-Dimensional Shapes

Covering and Surrounding Practice Answers

CONSTRUCTION / HOUSING

Find the area and perimeter of each figure. Round to the nearest tenth if necessary.

FSA 7 th Grade Math. MAFS.7.G.1.1 Level 2. MAFS.7.G.1.1 Level 3. MAFS.7.G.1.1 Level 3. MAFS.7.G.1.2 Level 2. MAFS.7.G.1.1 Level 4

MEA 501 LESSON _NOTES Period. CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 301 Compute the perimeter of polygons when all

Concept: Pythagorean Theorem Name:

Daily Warmup. - x 2 + x x 2 + x Questions from HW?? (7x - 39) (3x + 17) 1. BD bisects ABC. Find the m ABC.

Analytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6

8 th Grade Domain 3: Geometry (28%)

2003 Exit 13) Use the information in each diagram to find the pair of similar polygons. A B C D

Transcription:

Lesson 6.1 Skills Practice Name Date Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem Vocabulary Match each definition to its corresponding term. 1. A mathematical statement that can be proven using definitions, a. diagonal of a postulates, and other theorems. square 2. Either of the two shorter sides of a right triangle. b. right triangle 3. An angle that has a measure of 90 and is indicated by a c. Pythagorean square drawn at the corner formed by the angle. Theorem 4. A series of steps used to prove the validity of an if-then d. right angle statement. 5. A line segment connecting opposite vertices of a square. e. theorem 6. If a and b are the lengths of the legs of a right triangle and c is f. leg the length of the hypotenuse, then a 2 1 b 2 5 c 2. 7. A mathematical statement that cannot be proven but is g. postulate considered to be true. 8. A triangle with a right angle. h. hypotenuse Chapter 6 Skills Practice 533

Lesson 6.1 Skills Practice page 2 9. The longest side of a right triangle. This side is always i. proof opposite the right angle in a right triangle. Problem Set The side lengths of a right triangle are given. Determine which length is the hypotenuse. Use the Pythagorean Theorem to verify each length. 1. 9, 12, 15 The length of the hypotenuse is 15. 2. 10, 26, 24 9 2 1 12 2 5 15 2 81 1 144 5 225 225 5 225 3. 20, 12, 16 4. 6, 8, 10 534 Chapter 6 Skills Practice

Lesson 6.1 Skills Practice page 3 Name Date 5. 25, 15, 20 6. 15, 36, 39 Calculate the length of the hypotenuse of each given triangle. 7. 8. 24 14 48 18 c 2 5 a 2 1 b 2 c 2 5 24 2 1 18 2 c 2 5 576 1 324 c 2 5 900 c 5 900 c 5 30 Chapter 6 Skills Practice 535

Lesson 6.1 Skills Practice page 4 9. 1.5 2 10. 9 12 11. 6 12. 18 10 5 536 Chapter 6 Skills Practice

Lesson 6.1 Skills Practice page 5 Name Date Answer each question using the scenario. 13. Clayton is responsible for changing the broken light bulb in a streetlamp. The streetlamp is 12 feet high. Clayton places the base of his ladder 4 feet from the base of the streetlamp. Clayton can extend his ladder from 10 feet to 14 feet. How long must his ladder be to reach the top of the streetlamp? Round your answer to the nearest hundredth. 12 ft 4 ft c 2 5 a 2 1 b 2 c 2 5 4 2 1 12 2 c 2 5 16 1 144 c 2 5 160 c < 12.65 Clayton must extend his ladder about 12.65 feet. Chapter 6 Skills Practice 537

Lesson 6.1 Skills Practice page 6 14. Jada is helping to build a swing set at the community park. The swing bar at the top of the set should be 8 feet from the ground. The base of the support beam extends 3 feet from the plane of the swing bar. How long should each support beam be? Round your answer to the nearest tenth. 8 ft 3 ft 538 Chapter 6 Skills Practice

Lesson 6.1 Skills Practice page 7 Name Date 15. Perry wants to replace the net on his basketball hoop. The hoop is 10 feet high. Perry places his ladder 4 feet from the base of the hoop. How long must his ladder be to reach the hoop? Round your answer to the nearest hundredth. 10 ft 4 ft Chapter 6 Skills Practice 539

Lesson 6.1 Skills Practice page 8 16. Ling wants to create a diagonal path through her flower garden using stepping stones. She would like to place one stone every 2 feet. How many stepping stones does she need? 12 ft 16 ft 540 Chapter 6 Skills Practice

Lesson 6.1 Skills Practice page 9 Name Date Calculate the length of the missing side of each given triangle. 17. 6 15 18. 22 24 c 2 5 a 2 1 b 2 15 2 5 6 2 1 b 2 225 2 36 5 b 2 189 5 b 2 13.75 < b 19. 4 8 20. 5 7 Chapter 6 Skills Practice 541

Lesson 6.1 Skills Practice page 10 21. 12 22. 8 18 14 23. 6 24. 8 10 3 542 Chapter 6 Skills Practice

Lesson 6.2 Skills Practice Name Date Can That Be Right? The Converse of the Pythagorean Theorem Vocabulary Write the term that best completes the statement. 1. The states: If a 2 1 b 2 5 c 2, then the triangle is a right triangle. 2. The of a theorem is created when the if-then parts of the theorem are exchanged. 3. A set of three positive integers a, b, and c that satisfy the equation a 2 1 b 2 5 c 2 is a(n). Problem Set Determine whether each triangle with the given side lengths is a right triangle. 1. 8, 15, 17 c 2 5 a 2 1 b 2 2. 6, 9, 14 17 2 5 15 2 1 8 2 289 5 225 1 64 289 5 289 This is a right triangle. Chapter 6 Skills Practice 543

Lesson 6.2 Skills Practice page 2 3. 12, 15, 18 4. 5, 12, 13 5. 6, 8, 10 6. 9, 12, 16 544 Chapter 6 Skills Practice

Lesson 6.2 Skills Practice page 3 Name Date Answer each question using the scenario. 7. A computer monitor is sold by the diagonal length of the screen. A computer monitor has a 15-inch screen. The screen has a width of 13 inches. What is the height of the screen? Round your answer to the nearest tenth. a 2 1 b 2 5 c 2 a 2 1 13 2 5 15 2 a 2 1 169 5 225 a 2 5 56 a 5 56 a < 7.5 The height of the computer monitor screen is about 7.5 inches. Chapter 6 Skills Practice 545

Lesson 6.2 Skills Practice page 4 8. Luisa is building a sand box in her backyard. She places four pieces of wood in a rectangle to form the frame. The rectangle is 4 feet long and 3 feet wide. How can she use a measuring tape to make sure that the corners of the frame will be right angles? 546 Chapter 6 Skills Practice

Lesson 6.2 Skills Practice page 5 Name Date 9. Firefighters need to cross from the roof of a 25-feet-tall building to the roof of a 35-feet-tall building by using a ladder. The buildings are 20 feet apart. What minimum length does the ladder need to be in order to span the two buildings? Ladder 35 ft 25 ft 20 ft Chapter 6 Skills Practice 547

Lesson 6.2 Skills Practice page 6 10. Chen is building a ramp for his remote control car. He wants the end of the ramp to extend 4 feet from the base of the ramp. The base of the ramp is 18 inches high. How long should the piece of wood for the ramp be? Round your answer to the nearest tenth. 18 in. 4 ft 548 Chapter 6 Skills Practice

Lesson 6.2 Skills Practice page 7 Name Date 11. Perry wants to use a 12-foot ladder to reach a shelf that is 11 feet above the ground. How far from the wall should Perry place the base of the ladder so that the top of the ladder reaches the shelf? Round your answer to the nearest tenth. 12. Lea walks to soccer practice on Saturday. She leaves her home and walks 6 blocks north. Lea then turns east and walks 4 blocks to the soccer field. How far is the soccer field from Lea s home? Round your answer to the nearest whole number. Chapter 6 Skills Practice 549

Lesson 6.2 Skills Practice page 8 Calculate the length of the segment that connects the points in each. Write your answer as a radical if necessary. 13. 14. 4 3 a 2 1 b 2 5 c 2 3 2 1 4 2 5 c 2 9 1 16 5 c 2 25 5 c 2 25 5 c 5 5 c 550 Chapter 6 Skills Practice

Lesson 6.2 Skills Practice page 9 Name Date 15. 16. Chapter 6 Skills Practice 551

Lesson 6.2 Skills Practice page 10 17. 18. 552 Chapter 6 Skills Practice

Lesson 6.3 Skills Practice Name Date Pythagoras to the Rescue Solving for Unknown Lengths Problem Set Determine the length of the hypotenuse of each given triangle. 1. 2. 6 10 c 24 c 6 c 2 5 10 2 1 24 2 c 2 5 100 1 576 c 2 5 676 c 5 676 c 5 26 The length of the hypotenuse is 26 units. Chapter 6 Skills Practice 553

Lesson 6.3 Skills Practice page 2 3. 4. 4 c 4 c 7.5 7 554 Chapter 6 Skills Practice

Lesson 6.3 Skills Practice page 3 Name Date 5. 20 6. 4.5 c c 20 20 Chapter 6 Skills Practice 555

Lesson 6.3 Skills Practice page 4 Determine each unknown leg length. 7. 8. 12 20 a 13 11 b 12 2 1 b 2 5 20 2 144 1 b 2 5 400 b 2 5 400 2 144 b 2 5 256 b 5 256 b 5 16 The length of the leg is 16 units. 556 Chapter 6 Skills Practice

Lesson 6.3 Skills Practice page 5 Name Date 9. 10. 9 17 b a 12 12 Chapter 6 Skills Practice 557

Lesson 6.3 Skills Practice page 6 11. 9 41 b 12. 33 55 a 558 Chapter 6 Skills Practice

Lesson 6.3 Skills Practice page 7 Name Date Use the Pythagorean Theorem to determine whether each given triangle is a right triangle. 13. 14. 24 6 17 25 7 15 6 2 1 15 2 0 17 2 36 1 225 0 289 261 fi 289 The triangle is not a right triangle. 15. 16. 2 11 9 3.75 4.25 8 Chapter 6 Skills Practice 559

Lesson 6.3 Skills Practice page 8 17. 18. 21 35 5 28 28 26 560 Chapter 6 Skills Practice

Lesson 6.3 Skills Practice page 9 Name Date Use the Pythagorean Theorem to calculate each unknown length. 19. The design for a bridge truss is shown. The distance between the horizontal beams is 24 feet. The distance between the vertical beams is 18 feet. Determine the length (x) of each diagonal brace. 18 ft 24 ft x 18 2 1 24 2 5 x 2 324 1 576 5 x 2 900 5 x 2 900 5 x 30 5 x Each diagonal brace is 30 feet long. Chapter 6 Skills Practice 561

Lesson 6.3 Skills Practice page 10 20. The Archery Team is practicing on the basketball court in the gymnasium. The court is 50 feet wide and 94 feet long. The archers are shooting at a target placed at one corner of the court while they stand in the corner diagonally across the court. Determine the distance of each practice shot. 562 Chapter 6 Skills Practice

Lesson 6.3 Skills Practice page 11 Name Date 21. The water company installed a 40-yard diagonal brace on a water tower between two vertical beams that are 12 yards apart as shown. Determine the height of each vertical beam. 40 yd 12 yd Chapter 6 Skills Practice 563

Lesson 6.3 Skills Practice page 12 22. The lengths of the legs of a right triangle are 15 meters each. Determine the length of the hypotenuse. 23. The length of the hypotenuse of a right triangle is 50 inches. Determine the length of the legs if each leg is the same length. 564 Chapter 6 Skills Practice

Lesson 6.3 Skills Practice page 13 Name Date 24. A rescue boat leaves Walker Dock and travels 18 miles due north to haul in a sailing vessel stranded in the middle of a lake. After attaching a cable, the rescue boat hauls the sailing vessel 80 miles due east to Blue Haven Dock. Determine the direct distance from Walker Dock to Blue Haven Dock. Chapter 6 Skills Practice 565

566 Chapter 6 Skills Practice

Lesson 6.4 Skills Practice Name Date Meeting Friends The Distance Between Two Points in a Coordinate System Problem Set Determine the distance between each given pair of points by graphing and connecting the points, creating a right triangle, and applying the Pythagorean Theorem. 1. (2, 2) and (8, 5) y c 2 5 a 2 1 b 2 8 6 c 2 5 6 2 1 3 2 4 c 2 5 36 1 9 8 6 4 2 2 2 2 4 6 8 x c 2 5 45 c 5 45 4 c < 6.71 6 The distance between (2, 2) and (8, 5) 8 is approximately 6.71 units. Chapter 6 Skills Practice 567

Lesson 6.4 Skills Practice page 2 2. (3, 7) and (7, 3) y 8 6 4 2 x 8 6 4 2 2 2 4 6 8 4 6 8 3. (26, 8) and (6, 3) y 8 6 4 8 6 4 2 2 2 4 6 2 4 6 8 x 8 568 Chapter 6 Skills Practice

Lesson 6.4 Skills Practice page 3 Name Date 4. (7, 5) and (3, 23) y 8 6 4 2 x 8 6 4 2 2 2 4 6 8 4 6 8 5. (24, 24) and (5, 8) y 8 6 4 8 6 4 2 2 2 4 2 4 6 8 x 6 8 Chapter 6 Skills Practice 569

Lesson 6.4 Skills Practice page 4 6. (29, 3) and (7, 5) y 8 6 4 2 x 8 6 4 2 2 2 4 6 8 4 6 8 7. (27, 3) and (8, 25) y 8 6 8 6 4 4 2 2 2 4 2 4 6 8 x 6 8 570 Chapter 6 Skills Practice

Lesson 6.4 Skills Practice page 5 Name Date 8. (29, 6) and (8, 1) y 8 6 4 2 x 8 6 4 2 2 4 2 6 8 4 6 8 Archaeologists map each item they find at a dig on a 1-foot by 1-foot coordinate grid. Calculate the distance between the given pair of objects on the coordinate grid. 9. Determine the distance between the spindle and the beads. 9 8 y c 2 5 a 2 1 b 2 c 2 5 4 2 1 3 2 7 6 5 4 3 2 spindle c 2 5 16 1 9 c 2 5 25 c 5 25 c 5 5 1 0 0 beads 1 2 3 4 5 6 7 8 9 x The distance between the spindle and the beads is 5 feet. Chapter 6 Skills Practice 571

Lesson 6.4 Skills Practice page 6 10. Determine the distance between the pottery shard and the axe head. 9 8 7 6 5 4 3 y axe head 2 1 0 0 pottery shard 1 2 3 4 5 6 7 8 9 x 11. Determine the distance between the coins and the beads. 9 y 8 7 6 5 4 3 2 1 0 0 beads coins 1 2 3 4 5 6 7 8 9 x 572 Chapter 6 Skills Practice

Lesson 6.4 Skills Practice page 7 Name Date 12. Determine the distance between the coins and the axe head. 9 8 7 6 y axe head 5 4 coins 3 2 1 0 0 1 2 3 4 5 6 7 8 9 x 13. Determine the distance between the mask and the beads. 9 y mask 8 7 6 5 4 3 2 1 0 0 beads 1 2 3 4 5 6 7 8 9 x Chapter 6 Skills Practice 573

Lesson 6.4 Skills Practice page 8 14. Determine the distance between the pottery shard and the beads. 9 y 8 7 6 5 4 3 2 1 0 0 pottery shard beads 1 2 3 4 5 6 7 8 9 x 15. Determine the distance between the spindle and the axe head. 9 8 7 y axe head 6 5 4 3 2 spindle 1 0 0 1 2 3 4 5 6 7 8 9 x 574 Chapter 6 Skills Practice

Lesson 6.4 Skills Practice page 9 Name Date 16. Determine the distance between the mask and the coins. 9 y mask 8 7 6 5 4 coins 3 2 1 0 0 1 2 3 4 5 6 7 8 9 x Chapter 6 Skills Practice 575

576 Chapter 6 Skills Practice

Lesson 6.5 Skills Practice Name Date Diagonally Diagonals in Two Dimensions Problem Set Determine the length of the diagonals in each given quadrilateral. 1. The quadrilateral is a square. A B c 2 5 a 2 1 b 2 15 ft c 2 5 15 2 1 15 2 c 2 5 225 1 225 D C c 2 5 450 c 5 450 c < 21.21 The length of diagonal AC is approximately 21.21 feet. The length of diagonal BD is approximately 21.21 feet. Chapter 6 Skills Practice 577

Lesson 6.5 Skills Practice page 2 2. The quadrilateral is a rectangle. E F 10 in. H 18 in. G 578 Chapter 6 Skills Practice

Lesson 6.5 Skills Practice page 3 Name Date 3. The quadrilateral is a parallelogram. 11 m J K 6 m N 8 m M Chapter 6 Skills Practice 579

Lesson 6.5 Skills Practice page 4 4. The quadrilateral is a trapezoid. 9 y 8 7 6 5 4 P Q 3 2 S R 1 0 0 1 2 3 4 5 6 7 8 9 x 580 Chapter 6 Skills Practice

Lesson 6.5 Skills Practice page 5 Name Date 5. The quadrilateral is an isosceles trapezoid. 9 y 8 7 6 5 4 3 W X 2 1 0 0 Z 1 2 3 4 5 6 7 8 9 Y x Chapter 6 Skills Practice 581

Lesson 6.5 Skills Practice page 6 6. The quadrilateral is a rhombus. 9 y 8 7 6 5 4 B G 3 2 M K 1 0 0 1 2 3 4 5 6 7 8 9 x 582 Chapter 6 Skills Practice

Lesson 6.5 Skills Practice page 7 Name Date Calculate the area of each shaded region. 7. The figure is composed of a circle and a rectangle. The diagonal of the rectangle is the same length as the diameter of the circle. 4 in. The area of the rectangle is: A 5 bh A 5 (4)(9) 9 in. A 5 36 in. 2 The length of the rectangle s diagonal is: c 2 5 a 2 1 b 2 c 2 5 4 2 1 9 2 c 2 5 16 1 81 c 2 5 97 c 5 97 c < 9.85 in. The area of the circle is: A 5 πr 2 A < (3.14)(4.93) 2 A < 76.32 in. 2 The area of the shaded region is approximately 76.32 2 36 5 40.32 in. 2. Chapter 6 Skills Practice 583

Lesson 6.5 Skills Practice page 8 8. The figure is composed of two squares. The length of the diagonal of the smaller square is equal to the width of the larger square. 10 ft 584 Chapter 6 Skills Practice

Lesson 6.5 Skills Practice page 9 Name Date 9. The figure is composed of a right triangle and a circle. The hypotenuse of the right triangle is the same length as the diameter of the circle. 5 m 12 m Chapter 6 Skills Practice 585

Lesson 6.5 Skills Practice page 10 10. The figure is composed of a right triangle and a square. The hypotenuse of the right triangle is one side of the square. 15 yd 20 yd 586 Chapter 6 Skills Practice

Lesson 6.5 Skills Practice page 11 Name Date 11. The figure is composed of a right triangle and a semi-circle. The hypotenuse of the right triangle is the same length as the diameter of the semi-circle. 5 ft 5 ft Chapter 6 Skills Practice 587

Lesson 6.5 Skills Practice page 12 12. The figure is composed of two right triangles. The hypotenuse of one right triangle is the leg of the other right triangle. 3 cm 3 cm 4 cm 588 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice Name Date Two Dimensions Meet Three Dimensions Diagonals in Three Dimensions Problem Set Draw all of the edges you cannot see in each rectangular solid using dotted lines. Then draw a three-dimensional diagonal using a solid line. 1. 2. 3. 4. Chapter 6 Skills Practice 589

Lesson 6.6 Skills Practice page 2 5. 6. 590 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 3 Name Date Determine the length of the three-dimensional diagonal in the given rectangular solid using each Pythagorean Theorem. 7. 5 m 8 m 8 m Length of second leg: Length of diagonal: c 2 5 8 2 1 8 2 d 2 < 11.31 2 1 5 2 c 2 5 64 1 64 d 2 < 127.92 1 25 c 2 5 128 c 5 128 d 2 < 152.92 d < 152.92 c < 11.31 d < 12.37 The length of the three-dimensional diagonal in the rectangular solid is approximately 12.37 meters. Chapter 6 Skills Practice 591

Lesson 6.6 Skills Practice page 4 8. 10 in. 4 in. 1 in. 592 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 5 Name Date 9. 11 cm 6 cm 3 cm Chapter 6 Skills Practice 593

Lesson 6.6 Skills Practice page 6 10. 15 m 4 m 3 m 594 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 7 Name Date 11. 9 ft 12 ft 5 ft Chapter 6 Skills Practice 595

Lesson 6.6 Skills Practice page 8 12. 14 in. 7 in. 13 in. 596 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 9 Name Date Use the diagonals across the front face, the side face, and the top face of each given solid to determine the length of the three-dimensional diagonal. Use a formula. 13. 3" 8" 6" d 2 5 1 2 (32 1 6 2 1 8 2 ) d 2 5 1 (9 1 36 1 64) 2 d 2 5 1 2 (109) d 2 5 54.50 d 5 54.50 d < 7.38 The length of the three-dimensional diagonal is approximately 7.38 inches. Chapter 6 Skills Practice 597

Lesson 6.6 Skills Practice page 10 14. 9 m 3 m 10 m 598 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 11 Name Date 15. 8 ft 10 ft 12 ft Chapter 6 Skills Practice 599

Lesson 6.6 Skills Practice page 12 16. 6 m 5 m 6 m 600 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 13 Name Date 17. 8 yd 4 yd 10 yd Chapter 6 Skills Practice 601

Lesson 6.6 Skills Practice page 14 18. 3" 15" 13" 602 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 15 Name Date Use a formula to answer each question. 19. A packing company is in the planning stages of creating a box that includes a three-dimensional diagonal support inside the box. The box has a width of 5 feet, a length of 6 feet, and a height of 8 feet. How long will the diagonal support need to be? d 2 5 5 2 1 6 2 1 8 2 d 2 5 25 1 36 1 64 d 2 5 125 d 5 125 d < 11.18 The diagonal support will need to be approximately 11.18 feet. 20. A plumber needs to transport a 12-foot pipe to a jobsite. The interior of his van is 90 inches in length, 40 inches in width, and 40 inches in height. Will the pipe fit inside his van? Chapter 6 Skills Practice 603

Lesson 6.6 Skills Practice page 16 21. You are landscaping the flower beds in your front yard. You choose to plant a tree that measures 5 feet from the root ball to the top. The interior of your car is 60 inches in length, 45 inches in width, and 40 inches in height. Will the tree fit inside your car? 22. Julian is constructing a box for actors to stand on during a school play. To make the box stronger he decides to include diagonals on all sides of the box and a three-dimensional diagonal through the center of the box. The diagonals across the front and back of the box are each 2 feet, the diagonals across the sides of the box are each 3 feet, and the diagonals across the top and bottom of the box are each 7 feet. How long is the diagonal through the center of the box? 604 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 17 Name Date 23. Carmen has a cardboard box. The length of the diagonal across the front of the box is 9 inches. The length of the diagonal across the side of the box is 7 inches. The length of the diagonal across the top of the box is 5 inches. Carmen wants to place a 10-inch stick into the box and be able to close the lid. Will the stick fit inside the box? Chapter 6 Skills Practice 605

Lesson 6.6 Skills Practice page 18 24. A technician needs to pack a television in a cardboard box. The length of the diagonal across the front of the box is 17 inches. The length of the diagonal across the side of the box is 19 inches. The length of the diagonal across the top of the box is 20 inches. The three-dimensional diagonal of the television is 24 inches. Will the television fit in the box? Determine each unknown measurement. 25. A rectangular box has a length of 8 inches and a width of 5 inches. The length of the threedimensional diagonal of the box is 12 inches. What is the height of the box? d 2 5 l 2 1 w 2 1 h 2 12 2 5 8 2 1 5 2 1 h 2 144 5 64 1 25 1 h 2 55 5 h 2 55 5 h 7.42 < h The height of the box is approximately 7.42 inches. 606 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 19 Name Date 26. The length of the diagonal across the front of a rectangular box is 6 feet, and the length of the diagonal across the top of the box is 9 feet. The length of the three-dimensional diagonal is 14 feet. What is the length of the diagonal across the side of the box? 27. A rectangular box has a length of 7 feet and a height of 11 feet. The length of the three-dimensional diagonal of the box is 20 feet. What is the width of the box? Chapter 6 Skills Practice 607

Lesson 6.6 Skills Practice page 20 28. The length of the diagonal across the side of a rectangular box is 16 centimeters, and the length of the diagonal across the top of the box is 18 centimeters. The length of the three-dimensional diagonal is 20 centimeters. What is the length of the diagonal across the front of the box? 29. A rectangular box has a height of 3 feet and a width of 4 feet. The length of the three-dimensional diagonal of the box is 13 feet. What is the length of the box? 608 Chapter 6 Skills Practice

Lesson 6.6 Skills Practice page 21 Name Date 30. The length of the diagonal across the front of a rectangular box is 30 inches, and the length of the diagonal across the side of the box is 30 inches. The length of the three-dimensional diagonal is 40 inches. What is the length of the diagonal across the top of the box? Chapter 6 Skills Practice 609

610 Chapter 6 Skills Practice