Question

two triangles are congruent. if they are, state by what theorem they are congruent. the
c. congruent by sss
d. not congruent
two triangles are congruent. if they are, state by what theorem they are congruent. the
c. congruent by sss
d. not congruent

Explanation:

Step1: Recall congruence theorems

Congruence theorems for triangles include SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side).

Step2: Analyze the given triangles

In the first pair of triangles, we have two angles ($105^{\circ}$ and $35^{\circ}$) and the included side ($15$ m) equal in both triangles. This satisfies the ASA (Angle - Side - Angle) congruence theorem. In the second pair of triangles, we also have two angles ($105^{\circ}$ and $35^{\circ}$) and the included side ($10$ m) equal in both triangles, which satisfies the ASA congruence theorem.

Answer:

They are congruent by ASA.