Question

Prove the Pythagorean Theorem using similar triangles. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. Be sure to create and name the appropriate geometric figures.

Answer 1

For the answer to the question above asking to prove the Pythagorean Theorem using similar triangles. The Pythagorean Theorem states that in a right triangle, 
A right triangle consists of two sides called the legs and one side called the hypotenuse (c²) . The hypotenuse (c²) is the longest side and is opposite the right angle.

⇒ α² + β² = c² 

"In any right triangle ( 90° angle) , the sum of the squared lengths of the two legs is equal to the squared length of the hypotenuse."

For example:  Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are 3 inches and 4 inches.  
c2 = a2+ b2
c2  = 32+ 42
c2 = 9+16
c2 = 15
c = sqrt25
c=5