Answer: To prove that triangle ABE is congruent to triangle CBD, we will use the SAS (Side-Angle-Side) Congruence Theorem.
This theorem states that if two triangles have two sides and the included angle congruent, then the triangles are congruent.
Given:
BE ≅ BD (congruent sides)
AD ≅ CE (congruent sides)
We have congruent sides AB and BC, and congruent angles A and C (included angles)
By SAS congruence theorem, we can prove that:
Triangle ABE ≅ triangle CBD
Therefore, triangle ABE is congruent to triangle CBD
Alternatively, if we use the ASA (Angle-Side-Angle) congruence theorem, where we have congruent angles and congruent sides between those angles, we can also prove that triangle ABE ≅ triangle CBD
Explanation: