February 10, 2014
8-2: Pythagorean Theorem
Hypotenuse - side opposite
the right angle (Longest Side)
Legs - sides adjacent to right
angle
Pythagorean Theorem
If ∆ABC is a right ∆,
then a2 +b2 =c2
February 10, 2014
Example 1)
a +b =c
2
2
2
a2 + b 2 = c2
February 10, 2014
Converse of the Pythagorean Theorem:
If a2 +b2 =c2, then ∆ABC is a
right triangle.
A Pythagorean Triple is a set of three numbers
a, b, and c that satisfy a2 +b2 =c2.
February 10, 2014
Pythagorean Inequality Theorems:
1. (8.6) - [Less Than] Theorem
If c2 < a2 + b2 , then ∆ABC
is ACUTE
2. (8.7) - [Greater Than] Theorem:
If c2 > a2 + b2 , then ∆ABC
is OBTUSE
February 10, 2014
Step #1: Can the measures form a triangle?
yes it is a triangle...but what kind?
Step #2: Classify the triangle by using the
pythagorean inequality theorems.
February 10, 2014
b. 9, 40, 41
February 10, 2014
February 10, 2014
HW:
P 552 # 9-12, 15, 21-26