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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

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

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

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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

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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

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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 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

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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

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Chapter 10 143 Glencoe Algebra 1

Study Guide and Intervention

The Pythagorean Theorem

The Pythagorean Theorem The side opposite the right angle in a right triangle is called the hypotenuse. This side is always the longest side of a right triangle. The other two sides are called the legs of the triangle. To find the length of any side of a right triangle, given the lengths of the other two sides, you can use the Pythagorean Theorem.

Pythagorean Theorem

If a and b are the measures of the legs of a right triangle and c is the measure of the hypotenuse, then c2 = a 2 + b 2 C B Ab a c

Find the length of the missing side.

c 2 = a 2 + b 2

Pythagorean Theorem

c 2 = 5 2 + 12 2 a =

5 and b = 12

c 2 = 169 Simplify. c = ⎷ 169 Take the square root of each side. c = 13

The length of the hypotenuse is 13.

Exercises

Find the length of each missing side. If necessary, round to the nearest hundredth.

1. 2. 3.

25
25
c 100
110
a40 30
c 12 5 14 8 D 415
89
5

Example

4. 5. 6.

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Chapter 10 144 Glencoe Algebra 1

Study Guide and Intervention (continued)

The Pythagorean Theorem

Right Triangles If a and b are the measures of the shorter sides of a triangle, c is the measure of the longest side, and c 2 = a 2 + b 2 , then the triangle is a right triangle. Determine whether the following side measures form right triangles. a. 10, 12, 14 Since the measure of the longest side is 14, let c = 14, a = 10, and b = 12. c 2 = a 2 + b 2

Pythagorean Theorem

14 2 ? 10 2 + 12 2 a = 10, b = 12, c = 14

196 ? 100 + 144 Multiply.

196 ≠ 244 Add.

Since c

2 ≠ a 2 + b 2 , the triangle is not a right triangle. b. 7, 24, 25 Since the measure of the longest side is 25, let c = 25, a = 7, and b = 24. c 2 = a 2 + b 2

Pythagorean Theorem

25
2 ? 7 2 + 24 2 a = 7, b = 24, c = 25

625 ? 49 + 576 Multiply.

625 = 625 Add.

Since c

2 = a 2 + b 2 , the triangle is a right triangle.

Exercises

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

1. 14, 48, 50 2. 6, 8, 10 3. 8, 8, 10

4. 90, 120, 150 5. 15, 20, 25 6. 4, 8, 4 ⎷ 5

7. 2, 2, ⎷ 8 8. 4, 4, ⎷ 20 9. 25, 30, 35

10. 24, 36, 48 11. 18, 80, 82 12. 150, 200, 250

13. 100, 200, 300 14. 500, 1200, 1300 15. 700, 1000, 1300

Example

10-5

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