Given: AB ≅ AE; BC ≅ DE Prove: ∠ACD ≅ ∠ADC

Triangles A B E has 2 lines coming down from point A to points C and D to form triangles A B C, A C D, and A D E. The lengths of B C and D E are congruent. The lengths of A B and A E are congruent.
Complete the paragraph proof.

We are given AB ≅ AE and BC ≅ DE. This means ABE is an isosceles triangle. Base angles in an isosceles triangle are congruent based on the isosceles triangle theorem, so ∠ABE ≅ ∠AEB. We can then determine △ABC ≅ △AED by
. Because of CPCTC, segment AC is congruent to segment
. Triangle ACD is an isosceles triangle based on the definition of isosceles triangle. Therefore, based on the isosceles triangle theorem, ∠ACD ≅ ∠ADC.