Converse of Pythagorean Theorem

[nycmathguy]

A. What is the Converse of the Pythagorean Theorem?

B. Provide a simple example.

 

[MathLover1]

The converse of the Pythagorean Theorem states that if the square of the third side of a triangle is equivalent to the sum of its two shorter sides, then it must be a right triangle.

example:

Check whether a triangle with side lengths 6 cm, 10 cm, and 8 cm is a right triangle.

10^2=6^2+8^2
100=36+64
100=100
Since the square of the length of the longest side is the sum of the squares of the other two sides, by the converse of the Pythagorean Theorem, the triangle is a right triangle.

 

[nycmathguy]

The converse of the Pythagorean Theorem states that if the square of the third side of a triangle is equivalent to the sum of its two shorter sides, then it must be a right triangle.

example:

Check whether a triangle with side lengths 6 cm, 10 cm, and 8 cm is a right triangle.

10^2=6^2+8^2
100=36+64
100=100
Since the square of the length of the longest side is the sum of the squares of the other two sides, by the converse of the Pythagorean Theorem, the triangle is a right triangle.

Very good. Easy.