Congruent Triangles(2)


Problem

For triangle ABC, AB is equal to AC and the angle CAB is 90 degrees. Take a point P on side AB. Then set Q on the line AC so that AP=AQ. Set point S as the intersection of line CP and BQ.
Prove that triangle CAP and BAQ are congruent.

Applet

How to use the applet.

This applet will help you to find congruent triangles.
  1. Drag point P, and set the location of P. Then press "Define point P" button.
  2. Choose the center of rotation from A, B, and C.
  3. Drag red points. The triangle APC will rotate around the center point.
Drag the red point.