Question

in the graphic below, δlae ≅ δkea by:
image of a quadrilateral with triangles δlae and δkea, and markings on sides and angles
options:
○ aas.
○ sss.
○ asa.
○ none of the choices are correct.
○ sas.

Explanation:

Step1: Identify the corresponding parts

In \(\triangle LAE\) and \(\triangle KEA\), we have \(LA = KE\) (marked with one tick), \(\angle L=\angle K\) (marked with \(x\)), and \(AE = EA\) (common side).

Step2: Recall the congruence criteria

The AAS (Angle - Angle - Side) congruence criterion 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, then the two triangles are congruent. Here, \(\angle L=\angle K\), another pair of angles (the angles opposite to the common side \(AE\)) can be considered (since the sum of angles in a triangle is \(180^{\circ}\) and two angles are already equal, the third angles are also equal), and \(AE\) is the non - included side.

Answer:

A. AAS