Converse of the Pythagorean Theorem




The converse of the Pythagorean Theorem helps you to find out if a triangle is right.

Basically, the converse states that whenever the sum of the squares of two sides equal to the square of the third side of the triangle, the triangle is a right triangle.

For example, given the following 3 sides , is the triangle right?

4, 5, 3

Is 52 = 42 + 32 ?

52 = 25 and 42 + 32 = 16 + 9 = 25

Since 25 = 25, the triangle is a right triangle.

Other examples:

1)

Do the sides 6, 8, and 10 form a right triangle?

Is 102 = 62 + 82 ?

102 = 100 and 62 + 82 = 36 + 64 = 100

Since 100 = 100, the triangle is a right triangle.

2)

Do the sides 9, 12, and 15 form a right triangle?

Is 152 = 92 + 122 ?

152 = 255 and 122 + 92 = 144 + 81 = 225

Since 255 = 255, the triangle is a right triangle.


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