Question

14 which construction can you use to prove the pythagorean theorem based on similarity of triangles?

Explanation:

To prove the Pythagorean Theorem using triangle - similarity, we construct the altitude from the right - angle vertex to the hypotenuse of a right - triangle. This divides the original right - triangle into two smaller right - triangles, all of which are similar to each other. By setting up ratios of corresponding sides of these similar triangles and performing algebraic manipulations, the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\) can be derived.

Answer:

Construct the altitude from the right - angle vertex to the hypotenuse.