Question

based on the given information, which of the following can be used to prove these triangles are congruent?
aas
hl
there is not enough information to prove these triangles are congruent.
sas

Explanation:

Step1: Recall congruence criteria

• AAS (Angle - Angle - Side) states that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.
• In \(\triangle ABC\) and \(\triangle DEC\), we have \(\angle A=\angle D = 40^{\circ}\), \(\angle ACB=\angle DCE\) (since \(\angle ACB = 180^{\circ}-(40^{\circ}+75^{\circ})=65^{\circ}\) and \(\angle DCE=180^{\circ}-(40^{\circ}+75^{\circ}) = 65^{\circ}\)), and \(BC = EC\) (given as marked).
• Here, the side \(BC\) (in \(\triangle ABC\)) and \(EC\) (in \(\triangle DEC\)) is a non - included side with respect to the two pairs of equal angles (\(\angle A\) and \(\angle D\), \(\angle ACB\) and \(\angle DCE\)).

Answer:

A. AAS