Question

Given: AB is parallel to CD and BD bisects AC.

Prove: triangle ABE is congruent to triangle CDE.

Answer 1

Check the picture below.

Answer 2

Given BD bisects AC and AB∥ CD , the Angle-Angle-Side (AAS) congruence theorem proves △ABE≅△CDE.

Given: AB ∥ CD and BD bisects AC .Proposition: △ABE≅△CDE

Proof:

Segment Bisector Property: Since BD bisects AC , we know that AD = CD . (Given)

Alternate Interior Angles Theorem: Since

AB ∥ CD and BD is transversal, we know that ∠ABE=∠CDE. (Corresponding angles)

Given: We are given that AB=CD.

AAS Congruence Theorem: By the Angle-Angle-Side (AAS) congruence theorem, we can conclude that △ABE≅△CDE. This is because we have two congruent angles (∠ABE=∠CDE) and a congruent side between them (AB=CD and AD=CD).

Conclusion: Therefore, we can prove that △ABE≅△CDE.