Question

Given: BD and AC bisect each other Prove: TriangleABE is congruent to TriangleCDE

Answer 1

Based on the definition of bisection and appropriate theorems, the proof that shows ΔABE ≅ ΔCDE is shown below.

What is the Definition of Bisection?

When two lines bisect each other, they divide each other into equal segments, that is congruent segments.

The proof that shows that triangles ABE and CDE are congruent is explained below:

Statement                                         Reasons                                  

1. BD and AC bisect each other      1. Given

2. AE ≅ CE and BE ≅ DE                 2. Definition of bisection

3. ∠AEB ≅ ∠CED                              3. Vertical angles theorem

4. ΔABE ≅ ΔCDE                              4. SAS congruence theorem

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