3.9

Pythagorean Theorem

And

Its Converse

3.9 – Pythagorean Theorem & Converse

Pythagorean Theorem In a RIGHT triangle

a

b

c

a + b = c2 2 2

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

3.9 – Pythagorean Theorem & Converse

Example: Find the length of the hypotenuse. Do they form a Pythag. Triple?

21

20

3.9 – Pythagorean Theorem & Converse

Find the missing side.

820

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!!!

3.9 – Pythagorean Theorem & Converse

Is the triangle a RIGHT triangle?

84

1385

3.9 – Pythagorean Theorem & Converse

Can we use Pythag.’s Theorem to tell us if a triangle is OBTUSE or ACUTE?

3.9 – Pythagorean Theorem & Converse

YES we can!!!!

If then the triangle is OBTUSE

If then the triangle is ACUTE

a + b < c2 2 2

a + b > c2 2 2

3.9 – Pythagorean Theorem & Converse

Classify the triangle whose sides are 6, 11, and 14 as acute, obtuse, or right

3.9 – Pythagorean Theorem & Converse

Classify the triangle whose sides are 7, 8, and 9 as acute, obtuse, or right