Question

1. can you use the asa postulate, the aas theorem, or both to prove the triangles congruent? a asa only b aas only c either asa or aas d neither

Explanation:

1. Recall ASA (Angle - Side - Angle) and AAS (Angle - Angle - Side) congruence criteria.

• ASA: Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
• AAS: Two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle.

1. Analyze the given triangles:

• The vertical angles formed by the intersecting sides are congruent (by the Vertical Angles Theorem). We have one pair of marked congruent sides (the sides with the tick marks) and two pairs of marked congruent angles (the angles with the arcs).
• If we consider the congruent side as a non - included side between the two angles, we can use AAS. Also, if we re - order the angles and the side, we can think of it as ASA. Let's see: The vertical angles are congruent, we have one pair of angles (the arcs) and one pair of sides (the tick marks). The two angles (one arc - marked angle, one vertical angle) and the included side (the tick - marked side) can be used for ASA, and also the two arc - marked angles and the non - included side (the tick - marked side) can be used for AAS. So we can use either ASA or AAS to prove the triangles congruent.

Answer:

C. either ASA or AAS