Given: Right △ACB, CD ⟂ AB

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

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