But what about the converse of the Pythagorean Theorem?
Are these right triangles?
We can use the Converse of the Pythagorean Theorem to find if the triangles are right triangles.
If the equation a2+b2=c2 is true, then we will have a right triangle.
For the first triangle:
For the second triangle:
To concrete examples of the converse are the Pythagorean triples:
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. A right triangle whose sides form a Pythagorean triple is called a Pythagorean triangle.
A primitive Pythagorean triple (PPT) is one in which a, b and c are pairwise coprime.
There is a great formula that will generate an infinite number of Pythagoren Triples that are integers (not fractions).
You get the Pythagorean Triple (10,24,26)
Substituting those numbers into the Pythagorean Theorem: