View attachment 8178
The question is shown above. The solution tells me that when I draw a line segment from Y to P (where P is a point on side WZ) such that the angle YPW is 135degrees, since sides XY and WZ are parallel to each other, the quadrilateral XYPW becomes a parallelogram ... but why? Why does XYPW become a parallelogram just because XY and WP are parallel?
The parallel sides XY and WP are not the
only reason why XYPW is a parallelogram; sides WX and PY are also parallel. They must be, in order for their explanation to make sense.
Perhaps, you were misled by their diagram of the trapezoid; it could be a lot better.
The blue shape for WXYZ needs to be more horizontally-symmetrical (i.e., they should have been more careful to draw the left half as a reflection of the right half)
They
definitely ought to have said something about angles WXY and XWZ, too. Are you sure that you posted all given information?
Each of the top angles is 135°
Each of the base angles is 45°
By the way, if you also connect points X and P, there's a way to answer the question without using symbols a and b.
Hint: Determine the measure of every interior angle, and then think about those three shapes sitting next to each other. :cool:
