Question

given the two triangles below. are they necessarily congruent? explain why or why not. choose the correct answer below. a. yes, aaa is sufficient for congruence. if two triangles are congruent, then their corresponding angles must be congruent. this means that if corresponding angles are congruent, then the triangles must be congruent. b. yes, aaa is sufficient for congruence. if corresponding angles are congruent, then corresponding sides must also be congruent. this means that aaa is equivalent to sss. c. no, aaa is not sufficient for congruence. one triangle might be larger than the other. d. no, aaa is not sufficient for congruence. it is not possible to say two triangles are congruent without knowing the three pairs of corresponding sides are congruent.

Explanation:

Step1: Recall congruence criteria

Congruent triangles have equal - sized corresponding sides and angles. AAA (angle - angle - angle) only gives information about the equality of angles.

Step2: Analyze AAA criterion

Two triangles with the same set of angle measures can be of different sizes. One can be a scaled - up or scaled - down version of the other. For example, a small equilateral triangle with side length 2 and a large equilateral triangle with side length 5 have the same angle measures (each angle is 60°), but they are not congruent.

Answer:

C. No, AAA is not sufficient for congruence. One triangle might be larger than the other