Question

PLEASE HELP!! Determine whether the triangles are congruent. If so, name the postulate or theorem that justifies your answer. If not, explain.

A. The triangles are congruent by the ASA Postulate.

B. The triangles are congruent by the AAS Theorem.

C. The triangles are not necessarily congruent. Not enough information provided.

D. The triangles are congruent by the SAS Postulate.

Answer 1

These angles are congruent by AAS Theorem because since the two triangles intersect the top angles will be the same measurement. It also shows that another side of one triangle is also congruent with the other side of the other triangle.

To simplify the triangles have to congruent sides. However, what makes the triangles congruent by AAS Postulate instead of ASA Postulate which many people confuse with each other is because the known sides that are congruent to each other is not on the line of the angle.

Basically the known sides are not on the same line as the known congruent angles.
For the angles to be ASA Postulate the known side has to be on the same line as the congruent angles.

Therefore the answer is B.