Question

can you conclude that triangle ghf is congruent to triangle gjk? explain. yes, by asa yes, by aas yes, by aaa not enough information given

Explanation:

Step1: Identify known angles and sides

We know $\angle H=\angle J = 90^{\circ}$ and $HG = GJ$ (marked segments). Also, $\angle HGF$ and $\angle JGK$ are vertical - angles, so $\angle HGF=\angle JGK$.

Step2: Apply congruence criterion

The Angle - Side - Angle (ASA) congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. Here, for $\triangle GHF$ and $\triangle GJK$, we have $\angle H=\angle J$, $HG = GJ$, and $\angle HGF=\angle JGK$.

Answer:

yes, by ASA