Prove, and apply in mathematical and real-world contexts, theorems involving similarity about triangles, including the following:

a. A line drawn parallel to one side of a triangle divides the other two sides into parts of equal proportion.

b. If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

c. The square of the hypotenuse of a right triangle is equal to the sum of squares of the other two sides.