Bisectors of two base angles of a triangle meet the opposite sides at $X$ and $Y$. If $XY \parallel$ base, the triangle is —

The bisector of an angle divides the opposite side in the ratio of the two adjacent sides (angle-bisector theorem). For both base bisectors to make $XY \parallel BC$, the equal-ratio condition forces the two sides on the base to be equal, so the triangle is isosceles.