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

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

Step-by-step 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.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.