if point C is the midpoint of both line BD and AE, what additional information would you need to be able to state that triangle ABC= triangle EDC by the SAS congruence theorem?

Question

A line BC=line DC
B Line AB= line ED
C angle abc = angle ECD
D angle a = angle e

Answer 1

To use the SAS (Side-Angle-Side) congruence theorem to state that triangle ABC is congruent to triangle EDC, we need to confirm two sides and the included angle between those sides for both triangles.

Given that point C is the midpoint of BD and AE, we already have:

1. \( BC = DC \) (because C is the midpoint of BD)
2. \( AC = EC \) (because C is the midpoint of AE)

To apply the SAS theorem, we also need the angle between the sides AC and BC that corresponds to angle EDC.

The options provided suggest different pieces of information regarding the sides or angles of the triangles.

To satisfy the SAS condition (where we need two sides and the included angle), we would require knowledge about the included angles. Here, the correct answer would be:

C) angle ABC = angle ECD

This would allow us to conclude that triangle ABC is congruent to triangle EDC by the SAS theorem, since we would then know two sides and the included angle are equal.