4.5 the converse of the pathagorean theorem

The converse of the Pythagorean Theorem, is true

Step-by-step explanation:

The Pythagorean theorem or Pythagoras's theorem is a statement about the sides of a right triangle.

If the lengths of the legs are a and b, and the length of the hypotenuse is c, then,

To prove that the converse of the Pythagorean Theorem,

By the Pythagorean Theorem,

But we know that and  

So,  

That is,

Since PQ and AB are lengths of sides, we can take positive square roots.

PQ=AB

That is, all the three sides of are congruent to the three sides of . So, the two triangles are congruent by the Side-Side-Side Congruence Property.

Since is congruent to and is a right triangle, must also be a right triangle.

This is a contradiction. Therefore, our assumption must be wrong.

Therefore the converse of the Pythagorean Theorem,

If a^2 + b^2 = c^2, then the triangle is a right triangle.