1. Pythagorean Theorem and Its Converse
Objective
To use the Pythagorean Theorem and its converse
Essential Understanding:
If you know the lengths of any two sides of a right triangle, you can find the length of the third side by using the Pythagorean Theorem.

2. Pythagorean Theorem Theorem: A conjecture that has been proved
In a right triangle, the sum of the square of the lengths of the legs equals the square of the length of the hypotenuse.
If a and b are the lengths of the legs, and c is the length of the hypotenuse, then a2 + b2 = c2. c a b

3. Examples
How high up a wall will a 20 foot ladder touch if the foot of the ladder is placed 5 feet from the wall? Find the approximate height 7 b c 8 11
wall
20 ft b
a2 + b2 = c2 6
72 + b2 = 112
a2 + b2 = c2
5 ft
49 + b2 = 121
a2 + b2 = c2
= c2
52 + b2 = 202
b2 = 72
= c2
25 + b2 = 400
b2 = 375
100 = c2
10 = c

4. Converse of Pythagorean Theorem
If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

5. Converse of Pythagorean Theorem
Given a right triangle then a c
a2 + b2 = c2
Converse of Pythagorean Theorem b
Converse:
Switch the if and then parts
Given 3 sides of triangle that satisfy
a2 + b2 = c2
then triangle is a right triangle

6. Leave answers in simplest radical form
Examples
Right Triangle? 10 24 8 7 26
p. 495: 7, 9, 11, even
Leave answers in simplest radical form
a2 + b2 = c2 4
= 262
a2 + b2 = c2
= 676
= 82
676 = 676
= 64
65 = 64
Yes No