The prove that AB ≡ CD is completed using the ASA congruence theorem
How to complete the proof
Statement Reason
AB ⊥ BC given
CD ⊥ CB given
∠ B ≡ ∠ C right angles are equal
BE ≡ EC definition of bisection
∠ AEB ≡ ∠ CED vertical angles are equal
Δ AEB ≡ Δ CED ASA congruence theorem
AB ≡ CD CPCTC