Download 1.6 Exploring the Pythagorean Theorem Notes

Unit 1: Square Roots & The Pythagorean Theorem
1.6 Exploring the Pythagorean Theorem
Math 8
MacLean
The Pythagorean Theorem is true for right triangles only!
To see which triangle is a right triangle, check to see if the area of the square on the
longest side is equal to the sum of the areas of the squares on the other two sides.
A = 225 cm2
A = 169 cm2
15 cm
13 cm
12 cm
7 cm
P
Q
5 cm
A = 144 cm2
A = 49 cm2
10 cm
A = 100 cm2
A = 25 cm2
a2 + b2 = c2
52 + 122 = 132
25 + 144 = 169
a2 + b2 = c2
72 + 102 = 152
49 + 100 ≠ 25
The Pythagorean Theorem applies to the triangle P, but not to triangle Q.
A set of three whole numbers that satisfy the Pythagorean Theorem is called a
Pythagorean triple. For example, the number combination 5 – 12 - 13 is a
Pythagorean triple because 52 + 122 = 132 and they are all whole numbers!
Try These:
1. Is this triangle a right triangle? Show your work to prove your answer.
13 cm
10 cm
8 cm
𝑎2 + 𝑏 2 = 𝑐 2
82 + 102 = 132
64 + 100 = 169
164 ≠ 169
No, it is not a right triangle.
It does not satisfy the Pythagorean Theorem.
2. Is a triangle with side lengths 5, 12, and 13 cm a right triangle? Is it a Pythagorean
Triple? Explain.
𝑎2 + 𝑏 2 = 𝑐 2
52 + 122 = 132
25 + 144 = 169
169 = 169
Yes, it is a right triangle.
It satisfies the Pythagorean Theorem.
It is also a Pythagorean Triple because it is three whole numbers.