Question

What is the triangles congruence theorem could you use to prove the triangle ADE is congruent to Triangle CDE

A) side angle side triangle congruence
B) angle side angle triangle congruence
C) side side side triangle congruence
D) side side angle triangle congruences ​

Answer 1

The triangle congruence theorem that can be used to prove triangle ADE is congruent to triangle CDE is side angle side triangle congruence (SAS).

Step-by-step explanation:

The triangle congruence theorem that can be used to prove triangle ADE is congruent to triangle CDE is side angle side triangle congruence (SAS).

1. We can prove the triangles are congruent by showing that two corresponding sides and the included angle of one triangle are congruent to the corresponding sides and included angle of the other triangle.
2. In this case, we can show that side AD is congruent to side CD, side DE is congruent to itself, and angle A is congruent to angle C (since they are vertically opposite angles).
3. Therefore, by using the SAS congruence criterion, we can conclude that triangle ADE is congruent to triangle CDE.

Answer 2

B) angle side angle triangle congruence

Step-by-step explanation:

In the diagram given, the two angles, <A and <E, and the included side, AE, are congruent to the corresponding two angles, <C and <E, and corresponding included side, CE.

Therefore, based on the ASA Congruence Theorem, we can conclude that both triangles are congruent to each other.