Question

can you conclude that these triangles are congruent?

Explanation:

Step1: Identify vertical angles

$\angle BAC$ and $\angle FAG$ are vertical angles. By the vertical angles theorem, $\angle BAC=\angle FAG$.

Step2: Check for congruent sides

From the diagram, $BA = GA$ (one mark) and $CA=FA$ (two marks).

Step3: Apply congruence criterion

We have two sides and the included angle (SAS - Side - Angle - Side congruence criterion). In $\triangle BAC$ and $\triangle GAF$, $BA = GA$, $\angle BAC=\angle GAF$, $CA = FA$. So, $\triangle BAC\cong\triangle GAF$ by SAS.

Answer:

Yes, the triangles are congruent.