Given: CA bisects ∠BAD, AB ⊥ BC and AD ⊥ DC . Prove: △ABC≅△ADC.

Answer 1

Hello Taylor!

If I understood correctly, then first let's call the angle BAC = CAD = α. From the statement we have angle ABC = 90° (AB ⊥ BC) and also angle ADC = 90° (AD ⊥ DC).

Then we have: angle BCA = ACD = 90 - α

We the have that:

AC = AC (the triangles share this size)

angle BCA = ACD

angle BAC = CAD

Then the triangles are congruent due to SAS