Answer:
B) Both apply
Step-by-step explanation:
The Angle-Side-Angle (ASA) Postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
The Angle-Angle-Side (AAS) Theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
In the given diagram, one angle and one side of one triangle are congruent to the corresponding angle and side in the other triangle.
Since the angles opposite the congruent sides are vertically opposite each other, they are also congruent.
When two angles of one triangle are congruent to two angles of another triangle, the third angles are also congruent because the sum of the interior angles of a triangle is always constant (180°).
So, since both triangles share congruence in (a) two angles and an included side, and (b) two angles and a non-included side, both the ASA Postulate and the AAS Theorem can be used to prove that the two triangles are congruent.
