Notes 5.4 – The Pythagorean Theorem

Pythagorean Theorem

For any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

leg (b)

The Converse of the Pythagorean Theorem is also true.

If the square of the length of one side of the triangle is equal to the sum of the squares of the lengths of the other two sides of a triangle, then the triangle is a right triangle.

Pythagorean Inequalities

If , is a RIGHT triangle

If , is an OBTUSE triangle

If , is an ACUTE triangle

Numbers that work in the Pythagorean Theorem are called Pythagorean Triples.

** Most Common Triples

3, 4, 5 (and multiples 6, 8, 10…..)

5, 12, 13 (and multiples 10, 24, 26…)

7, 24, 25 (and multiples 14, 48, 50….)

8, 15, 17 (and multiples 16, 30, 34….)

1, 1,