The converse of the Pythagorean theorem and its proof

This lesson brings in several possibly totally new concepts for 8th grade students: the converse of a theorem, and a proof by contradiction. So, I tried to take it slow.

First, we go through what is a converse of a theorem. Many mathematical theorems can be written in this format: If A, then B. (A and B are statements). The converse of a theorem is this: If B, then A. So, we just flip the statements A and B.

Sometimes a theorem is true, and its converse is not. In the case of the Pythagorean Theorem, its converse IS true.

In the video, we take a little bit of time to practice stating the converse of various statements. And then I go on to do the proof, by contradiction, of the converse of the Pythagorean Theorem.

The converse of the Pythagorean Theorem states that if we have a triangle with sides a, b, and c, and if the formula a² + b² = c² is true for its side lengths, then the triangle is a right triangle.

To prove that by contradiction, we assume the opposite: that if the formula a² + b² = c² is true for the side lengths of some triangle, then the triangle is NOT a right triangle.

Watch the video how it's done... we arrive at a contradiction, which then proves that the assumption is not true, so the opposite of the assumption IS true, which is what we wanted to prove.

This video deals with concepts in the standard 8.G.B.6. ("Explain a proof of the Pythagorean Theorem and its converse.")

See also

The Pythagorean Theorem — video lesson

Math Mammoth Grade 8 curriculum

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