EFGH is a square where X lies on EF and Y lies on GH such that EX=GY . Prove that triangle HEX and triangle FGY are congruent .
So HE and FG are equal (they're sides of the square).
Angles HEX and FGY are equal because they're corners of the square (and therefore equal).
Then you are given that EX = GY.
You have two sides and the included angle equal.
Take it from there.