Question 37
Let $ABCD$ be a trapezoid which is not a parallelogram. Let $P$ be the intersection of its diagonals and $Q$ the intersection of the extended nonparallel sides.
a. Draw through $P$ the line parallel to the bases, meeting the nonparallel sides at $X,Y$. Prove $XP=YP$.
b. Prove that $PQ$ meets the shorter base at its midpoint.
a. Draw through $P$ the line parallel to the bases, meeting the nonparallel sides at $X,Y$. Prove $XP=YP$.
b. Prove that $PQ$ meets the shorter base at its midpoint.