We have:
(1)
(2)
From (1) and (2)
In triangle ABC, draw line segments AQ and BP, where P and Q lie on sides AC and BC, respectively. Now draw PY parallel to AQ and QX parallel to BP, where X and Y line on AC and BC. Show that XY is parallel to AB.
I realize this is harder without a picture. Sorry.
I know that showing ABC and XYC are similar triangles would prove XY parallel to AB since they both share vertex C, but I don't know how. I know that the intersection of the sets of parallel lines for a parallelogram, but I don't know if that plays in or not.