A friend of mine posted this GRE geometry question and I gave it a look: https://i.stack.imgur.com/OwuhB.png (below) - I saw another question posted here which is similar to this but doesn't quite answer what I am asking.
The question is: is quantity A greater than quantity B, quantity B greater than quantity A, are they equal or is there not enough information to deduce this. And the only piece of information is the what's given below the figure: XY = YZ. The answer given is that they are equal.
From what I know if the areas are to be equal then their altitudes must be the same. WY can only be the altitude if XW = WZ (isosceles triangle). But this isn't stated. Can we deduce this from similarity principles? If so, how? If not, can we assume that the two triangles will have the same height because they share a common vertex?