example 1 verify right triangles tell whether the given triangle is a right triangle. a. b. let c...

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EXAMPLE 1 Verify right triangles l whether the given triangle is a right triangle. a . b . Let c represent the length of the longest side of the triangle. Check to see whether the side lengths satisfy the equation c 2 = a 2 + b 2 . 9 34 81 + 225 = ? = ? (3 34) 2 9 2 + 15 2 a . 306 = 306 b . 26 2 22 2 + 14 2 = ? 676 484 + 196 = ? 676 = 680 The triangle is a right triangle. The triangle is not a right triangle.

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Page 1: EXAMPLE 1 Verify right triangles Tell whether the given triangle is a right triangle. a. b. Let c represent the length of the longest side of the triangle

EXAMPLE 1 Verify right triangles

Tell whether the given triangle is a right triangle.a. b.

Let c represent the length of the longest side of the triangle. Check to see whether the side lengths satisfy the equation c2 = a2 + b2.

9 34 81 + 225=?

=?(3 34)2 92 + 152a.

306 = 306

b. 262 222 + 142=?

676 484 + 196=?

676 = 680

The triangle is a right triangle.

The triangle is not a right triangle.

Page 2: EXAMPLE 1 Verify right triangles Tell whether the given triangle is a right triangle. a. b. Let c represent the length of the longest side of the triangle

GUIDED PRACTICE for Example 1

Let c represent the length of the longest side of the triangle. Check to see whether the side lengths satisfy the equation c2 = a2 + b2.

64 = 64

The triangle is a right triangle.

1.

42 += (4 3 )282

64 = 16 + 16 3

4,4 3 , 8

Tell whether a triangle with the given side lengths is a right triangle.

Page 3: EXAMPLE 1 Verify right triangles Tell whether the given triangle is a right triangle. a. b. Let c represent the length of the longest side of the triangle

GUIDED PRACTICE for Example 1

121 + 100196 =

196 = 221

The triangle is not a right triangle.

2.

112 + 102=142

10, 11, and 14

c2 = a2 + b2

Let c represent the length of the longest side of the triangle.Check to see whether the side lengths satisfy the equation

Tell whether a triangle with the given side lengths is a right triangle.

Page 4: EXAMPLE 1 Verify right triangles Tell whether the given triangle is a right triangle. a. b. Let c represent the length of the longest side of the triangle

GUIDED PRACTICE for Example 1

The triangle is a right triangle.

3.

( 61)2 52 + 62=

61 25 + 36=

61 = 61

c2 = a2 + b2

5,6 and 61 Let c represent the length of the longest side of the triangle.Check to see whether the side lengths satisfy the equation

Tell whether a triangle with the given side lengths is a right triangle.