Question

Given that E is the midpoint of the line BC and that ∠B is congruent to ∠C, which of the following triangle congruence statements can be used to prove that line BA and line CD are congruent?

1. SSS Congruence
2. SAS COngruence
3. SSA Congruence
4.ASA Congruence

Answer 1

To prove that line segments BA and CD are congruent given that E is the midpoint of BC and angles at B and C are congruent, the SAS Congruence theorem is used. This is because there are two sides and the included angle that are congruent in the triangles formed.

Step-by-step explanation:

The question asks which triangle congruence statement can be used to prove that line segments BA and CD are congruent, given that E is the midpoint of line BC and that angles ∠B and ∠C are congruent. To determine this, we need to assess the criteria of each congruence postulate or theorem.

In the scenario provided, with E being the midpoint of BC, we know that BE is congruent to EC. Given that angles at B and C are also congruent and assuming that AB and AC (not mentioned but implied from context) are the other two sides of triangle ABC, then we have two equal sides and an included angle, which aligns with the criteria for SAS Congruence. Therefore, by SAS Congruence we can prove that triangle ABE is congruent to triangle ECD, and consequently that BA is congruent to CD.