8.1. Pythagorean Theorem and Pythagorean Triples http://www.ck12.org
Vocabulary
The two shorter sides of a right triangle (the sides that form the right angle) are thelegsand the longer side (the side
opposite the right angle) is thehypotenuse. ThePythagorean Theoremstates thata^2 +b^2 =c^2 , where the legs are
“a” and “b” and the hypotenuse is “c”. A combination of three numbers that makes the Pythagorean Theorem true
is called aPythagorean triple.
Guided Practice
- Find the missing side of the right triangle below.
- What is the diagonal of a rectangle with sides 10 and 16
√
5?
- Determine if the triangle below is a right triangle.
Answers:
- Here, we are given the hypotenuse and a leg. Let’s solve forb.
72 +b^2 = 142
49 +b^2 = 196
b^2 = 147
b=√
147 =
√
7 · 7 · 3 = 7
√
3
- For any square and rectangle, you can use the Pythagorean Theorem to find the length of a diagonal. Plug in the
sides to findd.
102 +
(
16
√
5
) 2
=d^2
100 + 1280 =d^2
1380 =d^2
d=√
1380 = 2
√
345
- Check to see if the three lengths satisfy the Pythagorean Theorem. Let the longest sides representc, in the
equation.
a^2 +b^2 =c^2
222 + 242 = 262
484 + 576 = 676
10606 = 676The triangle is not a right triangle.
Practice
Find the length of the missing side. Simplify all radicals.