Question

Which congruence theorem can be used to prove ABR = ACR?

Answer 1

I added a screenshot with the question.

Answer:
SAS

Explanation:
1- For a triangle to be congruent by SSS, each side in the first triangle must be congruent to the corresponding side in the second triangle
2- For a triangle to be congruent by SAS, two sides and the INCLUDED angle between them in the first triangle must be congruent to the two sides and the INCLUDED angle in the second triangle
3- For a triangle to be congruent by AAS, two angles and one side in the first triangle must be congruent to the corresponding two angles and side in the second triangle

Now, in the given figure, we have:
AR is a common side in both triangles
∠BAR = ∠CAR
AB = AC

We can note that:
Two sides and the included angle in the first triangle are congruent to the corresponding two sides and included angle in the second.
This means that:
The two triangles are congruent by SAS

Hope this helps :)