1. Pythagorean Theorem and It’s Converse
You have not lived a perfect day, unless you've done something for someone who will never be able to repay you. -- Ruth Smeltzer
Pythagorean Theorem and It’s Converse
Chapter 8 Section 2
Learning Goal: Learn/Apply the Pythagorean Th. and it’s converse

2. There are at least 80 different ways to prove the Pythagorean theorem9 16 25
There are at least 80 different ways to prove the Pythagorean theorem
Link to AgileMinds #13, Patty Paper Proof, 1-8

3. Pythagorean Theorem
Find the missing measures
12.7
√27

4. Converse of the Pythagorean Th.
Determine whether the sides of these triangles could form a right triangle
9, 12, 15
4√3, 4, 8
5, 8, 9
yes
yes no

5. Coordinate Geometry
Verify that ∆ABC is
a right ∆

6. Pythagorean Triple
A Pythagorean Triple is three whole numbers that satisfy the equation a2 + b2 = c2 .
(Remember our answers from before)
9, 12, 15
4√3, 4, 8
5, 8, 9
Are each of these 3 numbers a Pythagorean Triple?
rt. ∆
Yes
rt. ∆ No
not a rt. ∆ No
The most common Pythagorean Triple = 3-4-5

7. Pythagorean Triple
Determine whether 30, 40, and 50 are the sides of a right triangle. Then state whether they form a Pythagorean triple.
Yes, and Yes

8. Closer Look What do we know about a triangle with sides: 6, 8, 10?
6, 8, 12?
6, 8, 9? 10 6
Right Triangle
= 100 8 6 8 12
Obtuse Triangle
< 144 6 8 9
Acute Triangle
> 81

9. Converse of Pythagorean Th.
a2 + b2 = c2  Right Angle
c2 > a2 + b2 
c2 < a2 + b2 
Obtuse Angle
Acute Angle
What about . . .
1. 2, 3, 4
2. 7, 8, 5√3
>
Obtuse ∆
< 5√
Acute ∆

10. Homework
Pythagorean Theorem and Its Converse Worksheet