Question

in the figure, fb = ce and fd = ca. which statement explains the criterion that can be used to prove that △abc ≅ △def?
a) sss should be used because the three sides of △abc are congruent to the three sides of △def
b) hl should be used because the hypotenuse and leg of △abc are congruent to the hypotenuse and leg of △def
c) sas should be used because two sides and the included angle of △abc are congruent to two sides and the included angle of △def
d) asa should be used because two angles and the included side of △abc are congruent to two angles and the included side of △def

Explanation:

We are given that $FB = CE$, so $FB+FC=CE + FC$, which means $BC = EF$. Also, $\angle B=\angle E = 75^{\circ}$ and $BA=ED$. So, two - sides ($BC = EF$ and $BA = ED$) and the included angle ($\angle B=\angle E$) of $\triangle ABC$ are congruent to two - sides and the included angle of $\triangle DEF$. The SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer:

C) SAS should be used because two sides and the included angle of $\triangle ABC$ are congruent to two sides and the included angle of $\triangle DEF$