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 given information

From the diagram, \( \angle GHF = \angle GJK = 90^\circ \) (right angles), \( GH = GJ \) (marked congruent segments), and \( \angle HGF \) and \( \angle JGK \) are vertical angles, so \( \angle HGF=\angle JGK \).

Step2: Apply ASA congruence

ASA (Angle - Side - Angle) 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. For \( \triangle GHF \) and \( \triangle GJK \):

• \( \angle GHF=\angle GJK = 90^\circ \)
• \( GH = GJ \) (included side between the two angles)
• \( \angle HGF=\angle JGK \)

So by ASA, \( \triangle GHF\cong\triangle GJK \).

Answer:

A. yes, by ASA