1. Pythagorean Theorem And Its Converse
3.9
Pythagorean Theorem
And
Its Converse

2. 3.9 – Pythagorean Theorem & Converse
In a RIGHT triangle a b c
a + b = c 2

3. 3.9 – Pythagorean Theorem & Converse
Pythagorean Triple
A set of NON-zero numbers that make Pythagorean Theorem work.
Examples:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

4. 3.9 – Pythagorean Theorem & Converse
Example:
Find the length of the hypotenuse.
Do they form a Pythag. Triple? 21 20

5. 3.9 – Pythagorean Theorem & Converse
Find the missing side. 8 20

6. 3.9 – Pythagorean Theorem & Converse
Can you use Pythag.’s Theorem to figure out if a triangle is a RIGHT triangle or not?
Remember, Pythag.’s Theorem works for RIGHT triangles!!!

7. 3.9 – Pythagorean Theorem & Converse
Is the triangle a RIGHT triangle? 84 13 85

8. 3.9 – Pythagorean Theorem & Converse
Can we use Pythag.’s Theorem to tell us if a triangle is OBTUSE or ACUTE?

9. 3.9 – Pythagorean Theorem & Converse
YES we can!!!!
If then the triangle is OBTUSE
If then the triangle is ACUTE
a + b < c 2
a + b > c 2

10. 3.9 – Pythagorean Theorem & Converse
Classify the triangle whose sides are 6, 11, and 14 as acute, obtuse, or right

11. 3.9 – Pythagorean Theorem & Converse
Classify the triangle whose sides are 7, 8, and 9 as acute, obtuse, or right