Question

overlapping triangles
bc ≅ df
∠b ≅ ∠d
∠a ≅ ∠e
which of the following relationships proves why △cbe and △fda are congruent?
asa
aas
sss
sas

Explanation:

To determine the congruence of \(\triangle CBE\) and \(\triangle FDA\), we analyze the given information: \(\overline{BC} \cong \overline{DF}\) (a side), \(\angle B \cong \angle D\) (an angle), and \(\angle A \cong \angle E\) (another angle). By the AAS (Angle - Angle - Side) congruence criterion, if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, the triangles are congruent. Here, we have two angles (\(\angle B\cong\angle D\) and \(\angle E\cong\angle A\) which correspond to \(\angle CBE\) and \(\angle FDA\)'s angles) and a non - included side (\(\overline{BC}\cong\overline{DF}\)) that satisfy the AAS condition. ASA requires the side to be included between the two angles, SSS requires three sides, and SAS requires two sides and the included angle, so AAS is the correct criterion.

Answer:

B. AAS