1. 9.1 Pythagorean Theorem

2. What We Will Learn Use Pythagorean Thm Use converse of Pythagorean Thm
Classify Triangles

3. Needed Vocab
Pythagorean triple: set of three positive integers a, b, and c that satisfy the equation 𝑐 2 = 𝑎 2 + 𝑏 2

4. Exs. 1/2/3 Using Pythagorean Thm.
Find x
C is ALWAYS opposite the right angle and is the longest side, a and b don’t matter on order
𝑎 2 + 𝑏 2 = 𝑐 2
= 𝑥 2
25+144= 𝑥 2
169= 𝑥 2
169 = 𝑥 2
13=𝑥

5. Exs. 1/2/3 Continued Find x 𝑥 2 + 7 2 = 14 2 𝑥 2 +49=196 −49 −49
−49 −49
𝑥 2 =147
𝑥 2 = 147
𝑥= 49 ∗ 3
𝑥=7 3

6. Ex. 4 Converse of Pythagorean Thm
Is it a right triangle?
Remember c is ALWAYS opposite the right angle and longest side =
49+64=113
113=113
Yes

7. Your Practice Is it a right triangle? 15 2 + 36 2 = 4 95 2=
= 4 2 ∗
=16∗95
1521=1520 no

8. Ex. 5 Classifying Triangles
Key Concept:
If 𝑎 2 + 𝑏 2 = 𝑐 2 , then it is a right triangle
If 𝑎 2 + 𝑏 2 > 𝑐 2 , then it is an acute triangle
If 𝑎 2 + 𝑏 2 < 𝑐 2 , then it is an obtuse triangle
Verify that segments make a triangle first
Any two segments must add up to be longer than third side
Then plug into Pythagorean Thm to classify

9. Ex. 5 Classify
Verify that segments with lengths of 4.3 feet, 5.2 feet, and 6.1 feet form a triangle. Then classify the triangle.
>6.1, >5.2, >4.3
9.5> > >4.3
= 6.1 2
=37.21
45.53>37.21
acute