Given triangle abc with angle abc congruent to angle acb, which theorem could be used to prove that side ab is congruent to side ac?

a) vertical angles theorem
b) side side side theorem
c) angle angle side theorem
d) triangle sum theorem

You an apply either C)
To prove it draw the altitude from A that intersect BC in, say H.
In the 2 triangles ABH & ACH, Angle B=Angle C
Angle H1=H2=90, hence angle BAH=CAH
so Triangle ABH= Triangle ACH , since AH is a common side, H1 = H2 =90
& Angle BAH=Angle CAH