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.
AB ≅ AE and BC ≅ DE. The included angles ∠ABC and ∠AED are congruent because they correspond to the equal base angles of isosceles △ABE, so △ABC ≅ △AED by SAS. By CPCTC, the corresponding sides AC and AD are congruent, making △ACD isosceles.
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