Question

can you conclude that these triangles are congruent?

Explanation:

Step1: Check the ASA (Angle - Side - Angle) congruence criterion

In the two triangles \( \triangle HCG\) and \( \triangle FGC\), we have:

• \( \angle HCG=\angle FGC\) (given by the single arc markings)
• \( CG = GC\) (common side)
• \( \angle HGC=\angle FCG\) (given by the double arc markings)

Since two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, by the ASA (Angle - Side - Angle) congruence criterion, the two triangles are congruent.

Answer:

yes