Question

Which theorem proves that the triangles are congruent?
A) ASA
B) SAS
C) SSA
D) SSS

Answer 1

Hello!

Looking at the image above, we are given that side BE is congruent to side ED while side AE is congruent to side EC. This can be written as follows:

BE = ED
AE = EC

In this case, ∠1 and ∠2 can be classified as vertical angles. Vertical angles are the two angles on opposite sides of two intersecting lines. These angles are always congruent to one another. Consequently, ∠1 and ∠2 must also be congruent to one another. This can be written as follows:

∠1 = ∠2

We have now proven the congruency of two sides and one angle. Because the angle lies between the two sides, this implies the use of SAS (side-angle-side).

Therfore, the correct answer is B.

I hope this helps!

Answer 2

These triangles are congruent by side-angle-side congruence. The two pairs of tick marks indicate those sides congruent, and the included angles are congruent because they are vertical angles.

Answer:
B) SAS

Also, SSA (option C) is not a congruence postulate.