Question

can you conclude that these triangles are congruent?

Explanation:

Step1: Identify equal - parts

We have $\angle G=\angle C$ (marked angles) and $GB = CB$ (marked sides). Also, $\angle GBH=\angle CBF$ (vertically - opposite angles).

Step2: Apply congruence criterion

By the Angle - Side - Angle (ASA) congruence criterion, since we have two pairs of equal angles and the included side equal between $\triangle GBH$ and $\triangle CBF$, the two triangles are congruent.

Answer:

yes