The Pythagorean Theorem
Lesson 9.1
Using the Pythagorean Theorem
In a right triangle the sum of the squares of the legs
equals the square of the hypotenuse.
Pythagorean Triple
The set of 3 positive integers a, b, and c that satisfy the
equation c2 = a2 + b2.
3, 4, __
5, 12, __
8, 15, __
7, 24, __
6, 8, __ 10, 24, __ 16, 30, __ 14, 48, __
9, 12, __ 15, 36, __ 24, 45, __ 21, 72, __
12, 16, __ 20, 48, __ 32, 60, __ 28, 96, ___
Find the value of x. Then tell whether the side
lengths form a Pythagorean triple.
Find the value of x. Then tell whether the side
lengths form a Pythagorean triple.
The flagpole shown is supported by two wires. Use
the Pythagorean Theorem to approximate the
length of each wire.
Converse of the Pythagorean Theorem
If the square of the length of the longest side of a
triangle is equal to the sum of the squares of the
lengths of the other two sides, then the triangle is a
right triangle.
Tell whether each triangle is a right triangle.
4 5
8
2 30
9
12
14
Pythagorean Inequalities Theorem
For any △ABC, where c is the length of the longest side, the
following statements are true.
If c2 < a2 + b2, then △ABC is acute. If c2 > a2 + b2, then △ABC is obtuse.
Lesson 9.1 p 468; 1, 2, 4-32 even, 44-47