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.
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.
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.
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.
