Given: Right △ACB, CD ⟂ AB

Prove: (AC)(AC) = (AB)(AD)

Right △ACB, CD ⟂ AB
Definition of Similar Triangles
Given
AC/AB = AD/AC
△ACB ~ △ADC
(AC)(AC) = (AB)(AD)
Algebra
The altitude drawn to the hypotenuse of a right triangle creates three similar triangles.