1. 11.4 Pythagorean Theorem

2. Pythagorean Theorem hypotenuse c a For a right triangle: a2 + b2 = c2
legs

3. Find the missing length.
a2 + b2 = c2 c
= c2 3
= c2
25 = c2 4
√25 = √c2
5 = c

4. Find the missing length.
a2 + b2 = c2 c
= c2 11
= c2 2
√125 = c2
5√5 = c

5. Find the value of x. a2 + b2 = c2 (x+2)2 + (x)2 = (√10)2 x + 2 √10
We reject the
x=-3, b/c we cannot
have negative
dimensions
2x(x + 3) -2(x + 3) =0
(2x -2)(x + 3) =0
x = ___ or x =____ -3 1

6. Find the value of x. x + 3 a2 + b2 = c2 (x+1)2 + (x + 3)2 = (2 √5)2
x2 + 2x + 1+ x2 + 6x + 9 = (2 √5)2
2x2 + 8x + 10 = 20
2x2 + 8x -10 = 0
2x2 + 10x - 2x -10 = 0
2x(x + 5) - 2(x + 5) = 0 -5
X = ____ X = _______ 1
(2x – 2)(x + 5) = 0

7. Yes it is a right triangle!
Determine whether the triangle with the given side lengths is a right triangle.
7, 25, 24
a2 + b2 = c2
= 252
= 625
625 = 625
Yes it is a right triangle!

8. No, it is not a right triangle!
Determine whether the triangle with the given side lengths is a right triangle.
3, 8, 10
a2 + b2 = c2
= 102
= 100
73 = 100
No, it is not a right triangle!

9. Find the length of the third side.
a = 3, c = 7
b = ?
a2 + b2 = c2
32 + b2 = 72
9 + b2 = 49
√ √
b2 = 40
b = 2√10