Given:
∠E ≅ ∠A
EC = AC
Let's identify the theorem of the postulate that can be used to prove that triangle ACB is congruent to triangle BCD.
From the figure, we are given one pair of congruent angles and one pair of equal sides.
Also, by applying the vertical angles theorem, ∠DCE ≅ ∠BCA.
Here, we now have two pairs of equal angles and one pair of equal sides.
Since we have two pairs of congruent angles and the pairs included sides are equal, we can say the triangles are congruent using the Angle-Side-Angle (ASA) postulate.
The ASA postulate states that if two angles and the included side of one triangle are congruent to the two pairs and included side of another triangle, both triangles are congruent.
ANSWER:
ASA