Question

question 1 of 10
what else would need to be congruent to show that \\( \triangle a b c \cong \triangle d e f \\) by aas?
a. \\( \overline{a c} \cong \overline{d f} \\)
b. \\( \overline{b c} \cong \overline{e f} \\)
c. \\( \angle a \cong \angle c \\)
d. \\( \angle a \cong \angle d \\)

Explanation:

Step1: Recall AAS (Angle - Angle - Side) congruence criterion

AAS 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.
We already have \(AB = DE=10\) (given as side lengths) and \(\angle C=\angle F = 30^{\circ}\).

Step2: Analyze the angles and sides

We need another pair of angles. If \(\angle A\cong\angle D\), then we have two pairs of angles (\(\angle A\cong\angle D\) and \(\angle C\cong\angle F\)) and a non - included side (\(AB = DE\)).

Answer:

D. \(\angle A\cong\angle D\)