Included sides AE and BE need to be given as congruent to prove that triangle AEC is congruent to triangle BED by the Angle-Side-Angle (ASA) Congruence Theorem.
According to the Angle-Side-Angle (ASA) Congruence Theorem, if two angles and an included side of a triangle is congruent to corresponding two angles and an included side of another triangle, both triangles can be proven to be equal or congruent to each other.
We are know the following from the given image:
<AEC = <BED (vertical angles are congruent)
<EAC = <EBD (congruent angle)
This implies that two angles (<AEC and <EAC) in triangle AEC are congruent to two corresponding angles (<BED and <EBD) in triangle BED.
Therefore, to prove that both triangles are congruent by ASA, we need to be given that the included sides AE and BE are congruent.
Learn more about Angle-Side-Angle (ASA) Congruence Theorem here:
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