Explanation:
angle BCA ≅ angle ECD . . . . . . vertical angles are congruent
∆BCA ≅ ∆ECD . . . . . . . . . . . . . . SAS congruence theorem
BA ≅ ED . . . . . . . . . . . . . . . . . . . .CPCTC
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Based on the given congruences and the congruence of the vertical angles at C, we can invoke SAS congruence to show ∆BCA ≅ ∆ECD. Then the desired segments are congruent because corresponding parts of congruent triangles are congruent.
