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 .
It's a square so all angles and all sides are equal.
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.