Question

what additional piece of information would allow you to conclude that these triangles are congruent? select one: a. all of the given options b. <b = <e c. <a = <d and <c = <f d. ac = df

Explanation:

Step1: Recall congruence criteria

We have two - triangles with two pairs of corresponding sides equal (marked on the figure). The main congruence criteria for triangles are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze option b

If $\angle B=\angle E$, then by the SAS (Side - Angle - Side) congruence criterion, since we already have two pairs of corresponding sides equal, the two triangles $\triangle ABC$ and $\triangle DEF$ would be congruent.

Step3: Analyze option c

If $\angle A = \angle D$ and $\angle C=\angle F$, then by the AAS (Angle - Angle - Side) congruence criterion, the two triangles $\triangle ABC$ and $\triangle DEF$ would be congruent as we have two pairs of corresponding angles equal and a non - included side (the marked equal sides) equal.

Step4: Analyze option d

If $AC = DF$, then by the SSS (Side - Side - Side) congruence criterion, since we already have two other pairs of corresponding sides equal, the two triangles $\triangle ABC$ and $\triangle DEF$ would be congruent.

Answer:

A. all of the given options