Question

Which construction can you use to prove the Pythagorean Theorem based on similarity of triangles?

Answer 1

Answer: Draw perpendicular to the hypotenuse that goes through point of right angle.

Explanation:

Let ΔABC be any triangle right angled at B, then a line segment perpendicular to AC (hypotenuse) and name it point D such that in ΔABC and ΔABD, ∠B=∠ADB =90° and ∠A=∠A (common in both triangles) ,therefore by AA similarity criteria ΔABC is similar to ΔABD....> which can be use to prove the Pythagoras theorem.

Pythagoras theorem states that in any right angled triangle the square of the longest side is equal to the sum of the square of other two sides.

Answer 2

The construction that you can use to prove the Pythagorean Theorem based on similarity of triangles is 2nd construction. Please see the attached file.

To add, in mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It mentions that the sum of the squares of the other two sides is equal to the square of the hypotenuse (the side opposite the right angle).