Pythagorean Theorem and It’s Converse

Chapter 8 Section 2

Learning Goal: Learn/Apply the Pythagorean Th. 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

9

16

25There are at least 80 different ways to prove the

Pythagorean theorem

Link to AgileMinds #13, Patty Paper Proof, 1-8

Pythagorean Theorem Find the missing measures

√27

12.7

Converse of the Pythagorean Th.

Determine whether the sides of these triangles could form a right triangle

1. 9, 12, 15

2. 4√3, 4, 8

3. 5, 8, 9

yes

yes

no

Coordinate Geometry Verify that ∆ABC is

a right ∆

Pythagorean Triple A Pythagorean Triple is three whole

numbers that satisfy the equation a2 + b2 = c2 .(Remember our answers from before)

1. 9, 12, 15

2. 4√3, 4, 8

3. 5, 8, 9

rt. ∆

not a rt. ∆

Are each of these 3

numbers a Pythagorea

n Triple?

rt. ∆

Yes

No

No

The most common Pythagorean Triple = 3-4-5

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

6

8

10

Acute Triangle

Closer Look What do we know about a triangle

with sides:1. 6, 8, 10?

2. 6, 8, 12?

3. 6, 8, 9?

Right Triangle36 + 64 =

100

36 + 64 < 144

6

8

12Obtuse Triangle

36 + 64 > 816

8

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

42 32 + 22> Obtuse ∆5√3 72 +

82

< Acute ∆

Homework Pythagorean Theorem and Its

Converse Worksheet