[PDF] Chapter 8 Resource Masters PDF 8.2%20Worksheets.pdf

Study Guide and Intervention (continued) The Pythagorean Theorem and Its Converse Converse of the Pythagorean Theorem If the sum of the squares

Study Guide and Intervention The Pythagorean Theorem and Its Converse The Pythagorean Theorem In a right triangle, the sum of the squares of the lengths

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8-2 Study Guide and Intervention (continued) The Pythagorean Theorem and its Converse Converse of the Pythagorean Theorem If the sum of the squares o

[PDF] The Pythagorean Theorem and Its Converse

Example 1 Chapter 8 13 Glencoe Geometry Lesson 8-2 8-2 Study Guide and Intervention The Pythagorean Theorem and Its Converse NAME

[PDF] Geometry Homework 71 72 ANSWER KEYSpdf

7-2 Study Guide and Intervention The Pythagorean Theorem and Its Converse The Pythagorean Theorem In a right triangle, the sum of the squares of the

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10 jan 2014 · Study Guide and Intervention The Pythagorean Theorem The Pythagorean Theorem The side opposite the right angle in a right triangle is

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9-4 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

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10-4 Study Guide and Intervention - Do all The Pythagorean Theorem Use the Pythagorean Theorem In a right triangle, the sides adjacent to the right angle are

[PDF] Study Guide and Intervention - Prosser Career Academy

13 avr 2014 · Example 1 Chapter 8 13 Glencoe Geometry Lesson 8-2 8-2 Study Guide and Intervention The Pythagorean Theorem and Its Converse

[PDF] Study Guide and Intervention Workbook - Metrolina Regional

5 déc 2018 · Glencoe Geometry Study Guide and Intervention The Pythagorean Theorem and Its Converse The Pythagorean Theorem In a right triangle,

[PDF] Chapter 8 Resource Masters

Study Guide and Intervention (continued) The Pythagorean Theorem and Its Converse Converse of the Pythagorean Theorem If the sum of the squares

pdf NAME DATE PERIOD 8-2 Study Guide and Intervention

The Pythagorean Theorem and Its Converse The Pythagorean Theorem In a right triangle the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse If the three whole numbers ab and c satisfy the equation a2 + 2b = c2 then the numbers a b and c form a Pythagorean triple c a b A C B a Find a a 12

NAME DATE PERIOD 8-2 Study Guide and Intervention

The Pythagorean Theorem In a right triangle the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse If the three whole numbers a b and c satisfy the equation 2 + 2 = 2 then the numbers a b and c form a Pythagorean triple Example : Find a Find c ABC is a right triangle so 2 + 2 = 2

The Pythagorean Theorem and Its Converse

The Pythagorean TheoremIn a right triangle the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse 2ABCis a right triangle so a b2c2 Prove the Pythagorean Theorem With altitude CD each leg aand bis a geometric mean between hypotenuse cand the segment of the hypotenuse adjacent to that leg a c 2

Ms Schmidt's Classroom - Home

8-2 Study Guide and Intervention (continued) The Pythagorean Theorem and Its Converse Converse of the Pythagorean Theorem If the sum of the squares of the measures of the two shorter sides of a triangle equals the square of the measure of the longest side then the triangle is a right triangle

Chapter 8 Review Answers - Ms Johnson's Classroom Site

8-2 Study Guide and Intervention The Pythagorean Theorem and Its Converse Exercises Find x 65 = koo 28 11 QL3 96 15 16 33 z 25 28 Use a Pythagorean Triple to find x 45 24 17 Exercises Determine whether each set of measures can be the measures of the sides of a triangle If so classify the triangle as acute obtuse or right

Example 1

Chapter 813Glencoe Geometry

Lesson 8-2

8-2Study Guide and Intervention

The Pythagorean Theorem and Its Converse

NAME ______________________________________________ DATE ____________ PERIOD _____ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. The Pythagorean TheoremIn a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. ?ABCis a right triangle, so a 2 ?b 2?c 2

Prove the Pythagorean Theorem.

With altitude C

?D?, each leg aand bis a geometric mean between hypotenuse cand the segment of the hypotenuse adjacent to that leg. ac a y ?and ? bc b x ?, so a 2 ?cyand b 2 ?cx

Add the two equations and substitute c?y?xto get

a2 ?b 2 ?cy?cx?c(y?x) ?c 2 cy x a bh ACB D ca b

ACBa. Find a.

a 2 ?b 2 ?c 2

Pythagorean Theorem

a 2 ?12 2 ?13 2 b?12, c?13 a 2 ?144 ?169Simplify. a 2 ?25Subtract. a?5Take the positive square root of each side. a1213 ACB b. Find c. a 2 ?b 2 ?c 2

Pythagorean Theorem

20 2 ?30 2 ?c 2 a?20, b?30

400 ?900 ?c

Simplify.

1300 ?c

2 Add. ?1300? ?cTake the positive square root of each side.

36.1 ?cUse a calculator.

c 3020
ACB

Find x.

1. 2. 3.

4. 5. 6.

x 1128
x 3316
x 5 94
9 x 6525
x 159
x 33

Example 2

Exercises

Chapter 814Glencoe Geometry

Study Guide and Intervention(continued)

The Pythagorean Theorem and Its Converse

Converse of the Pythagorean TheoremIf the sum of the squares of the measures of the two shorter sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle. If the three whole numbers a,b, and csatisfy the equation a 2 ?b 2 ?c 2 , then the numbers a,b, and cform a If a 2 ?b 2 ?c 2 , then

Pythagorean triple.?ABCis a right triangle.

Determine whether ?PQRis a right triangle.

a 2 ?b 2 ?c 2

Pythagorean Theorem

10 2 ?(10?3?) 2 ?20 2 a?10, b?10?3?, c?20

100 ?300 ?400Simplify.

400 ?400?Add.

The sum of the squares of the two shorter sides equals the square of the longest side, so the triangle is a right triangle. Determine whether each set of measures can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean triple.

1.30, 40, 502.20, 30, 403.18, 24, 30

4.6, 8, 95.

3 7 4 7 5 7 ?6.10, 15, 20 7. ?5?,?12?,?13?8.2,?8?,?12?9.9, 40, 41 A familyof Pythagorean triples consists of multiples of known triples. For each Pythagorean triple, find two triples in the same family.

10.3, 4, 511.5, 12, 1312.7, 24, 25

10??320

10 QRP ca b AC B

Example

Exercises

Chapter 815Glencoe Geometry

Lesson 8-2

Skills Practice

The Pythagorean Theorem and Its Converse

Find x.

1. 2. 3.

4. 5. 6.

Determine whether ?STUis a right triangle for the given vertices. Explain.

7.S(5, 5),T(7, 3),U(3, 2)8.S(3, 3),T(5, 5),U(6, 0)

9.S(4, 6),T(9, 1),U(1, 3)10.S(0, 3),T(?2, 5),U(4, 7)

11.S(?3, 2),T(2, 7),U(?1, 1)12.S(2,?1),T(5, 4),U(6,?3)

Determine whether each set of measures can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean triple.

13.12, 16, 2014.16, 30, 3215.14, 48, 50

16. 2 5 4 5 6 5 ?17.2?6?,5,718.2?2?,2?7?,6 x 31
14 x 99
8 x 12.5 25
x 1232
x 1213
x 129

Chapter 816Glencoe Geometry

8-2Practice

The Pythagorean Theorem and Its Converse

Find x.

1. 2. 3.

4. 5. 6.

Determine whether ?GHIis a right triangle for the given vertices. Explain.

7.G(2, 7),H(3, 6),I(?4,?1)8.G(?6, 2),H(1, 12),I(?2, 1)

9.G(?2, 1),H(3,?1),I(?4,?4)10.G(?2, 4),H(4, 1),I(?1,?9)

Determine whether each set of measures can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean triple.

11.9, 40, 4112.7, 28, 2913.24, 32, 40

14. 9 5 1 52
?,315.? 1 3 ?,,116.,,? 4 7

17.CONSTRUCTIONThe bottom end of a ramp at a warehouse is

10 feet from the base of the main dock and is 11 feet long. How

high is the dock?

11 ft?dock

ramp 10 ft 2?3? 7 ?4? 72
?2? 3 x 2424
42
x 16 14 x 34
22
x 26
26
18 x 3421
x 1323
quotesdbs_dbs20.pdfusesText_26

[PDF] [PDF] Chapter 8 Resource Masters

Example 1

Chapter 813Glencoe Geometry

Lesson 8-2

8-2Study Guide and Intervention

The Pythagorean Theorem and Its Converse

Prove the Pythagorean Theorem.

With altitude C

Add the two equations and substitute c?y?xto get

ACBa. Find a.

Pythagorean Theorem

Pythagorean Theorem

400 ?900 ?c

Simplify.

1300 ?c

36.1 ?cUse a calculator.

Find x.

1. 2. 3.

4. 5. 6.

Example 2

Exercises

Chapter 814Glencoe Geometry

Study Guide and Intervention(continued)

The Pythagorean Theorem and Its Converse

Pythagorean triple.?ABCis a right triangle.

Determine whether ?PQRis a right triangle.

Pythagorean Theorem

100 ?300 ?400Simplify.

400 ?400?Add.

1.30, 40, 502.20, 30, 403.18, 24, 30

4.6, 8, 95.

10.3, 4, 511.5, 12, 1312.7, 24, 25

10??320

Example

Exercises

Chapter 815Glencoe Geometry

Lesson 8-2

Skills Practice

The Pythagorean Theorem and Its Converse

Find x.

1. 2. 3.

4. 5. 6.

7.S(5, 5),T(7, 3),U(3, 2)8.S(3, 3),T(5, 5),U(6, 0)

9.S(4, 6),T(9, 1),U(1, 3)10.S(0, 3),T(?2, 5),U(4, 7)

11.S(?3, 2),T(2, 7),U(?1, 1)12.S(2,?1),T(5, 4),U(6,?3)

13.12, 16, 2014.16, 30, 3215.14, 48, 50

Chapter 816Glencoe Geometry

8-2Practice

The Pythagorean Theorem and Its Converse

Find x.

1. 2. 3.

4. 5. 6.

7.G(2, 7),H(3, 6),I(?4,?1)8.G(?6, 2),H(1, 12),I(?2, 1)

9.G(?2, 1),H(3,?1),I(?4,?4)10.G(?2, 4),H(4, 1),I(?1,?9)

11.9, 40, 4112.7, 28, 2913.24, 32, 40

17.CONSTRUCTIONThe bottom end of a ramp at a warehouse is

10 feet from the base of the main dock and is 11 feet long. How

11 ft?dock