Question

PLEASE HELP!!

Given: C is the midpoint of segment AD and BE.

Which congruence pattern should you use to show the following triangles congruent? (There may be more than 1)
AAS
ASA
SSS
SAS

Answer 1

SAS

Explanation:

To determine the congruence pattern, we need to identify the congruent sides and angles in the given triangles.

Given that C is the midpoint of segment AD and BE, we can infer that:

1. AC = CD (since C is the midpoint of AD)

2. BC = CE (since C is the midpoint of BE)

We also know that angle ACB is shared by both triangles, so ∠ACB = ∠BCD.

Therefore, we have:

1. Two sides are congruent (AC = CD and BC = CE)

2. The included angle between these sides is congruent (∠ACB = ∠BCD)

This matches the SAS (Side-Angle-Side) congruence pattern. So, you should use the SAS congruence pattern to show that the triangles are congruent.