geometry proof?

Question

Given : WXYZ is a trapezoid, Q is midpoint of WX
Prove: triangle YQZ is isosceles
....Y-------Z

X-----Q-----W

Answer 1

Can't prove it because it isn't generally true.

There is no guarantee that YX = ZW or that angle YXW = ZWX unless WXYZ is an isosceles trapezoid.

http://en.wikipedia.org/wiki/Trapezoid

To prove this, consider the case where YZ is half the length of XW and angle YXW is a right angle. In that case YQZ is a right triangle with the right angle at Z.

If you do have an isosceles trapezoid, then you know that YX does equal ZW, and that angle YXW = ZWX so that YXQ and ZWQ are congruent triangles.

Answer 2

Were you given any angles? I haven't done geometry in like 10 years. But one thing I remember was something about parallel lines have the same opposite angles. Meaning angle yxq is the same as angle yx. If you know that there are 180 degrees in a straight angle, then you could find out the angle of the other two to see if it's isosceles.