Question

in the graphic below, $\triangle ghj \cong \triangle klj$ by:
image of two triangles with vertices g, h, j and k, l, j, with marked angles at g and k, and marked segments on gj and kj
\bigcirc sss.
\bigcirc aas.
\bigcirc sas.
\bigcirc asa.
\bigcirc none of the choices are correct.

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. So, \(\angle GJH=\angle KJL\) (vertical angles theorem).

Step2: Recall AAS (Angle - Angle - Side) congruence criterion

We have \(\angle G=\angle K\) (given as marked in the figure), \(\angle GJH = \angle KJL\) (from step 1), and \(GJ = KJ\) (given as marked in the figure). AAS 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.

Answer:

AAS.