Converse of the Pythagorean Theorem


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



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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