Question

analyzing diagrams
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 the given information

We know that \(GH = GJ\) (marked as equal), \(\angle FHG=\angle KJG = 90^{\circ}\), and \(\angle FGH=\angle KGJ\) (vertical angles are equal).

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

The AAS 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.
In \(\triangle GHF\) and \(\triangle GJK\):

• \(\angle FHG=\angle KJG\) (right angles, \(90^{\circ}\))
• \(\angle FGH=\angle KGJ\) (vertical angles)
• \(GH = GJ\) (given side)

Answer:

yes, by AAS