Question

question 5 of 45 which of the following must be true to prove △abc≅△def by the aas theorem? given: ∠a≅∠d, ac≅df a. ∠e≅∠f b. ∠c≅∠f c. ∠b≅∠e d. ∠b≅∠c

Explanation:

Step1: Recall AAS theorem

The AAS (Angle - Angle - Side) theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. Here we already have $\angle A\cong\angle D$ and $\overline{AC}\cong\overline{DF}$. We need another pair of non - included angles to be congruent.

Step2: Identify the correct angle pair

The non - included angles with respect to the given side and angle are $\angle C$ and $\angle F$. So for $\triangle ABC\cong\triangle DEF$ by AAS, we need $\angle C\cong\angle F$.

Answer:

B. $\angle C\cong\angle F$