Question 33
Let $SABCD$ be a pyramid with the apex $S$ and whose base $ABCD$ is a parallelogram. We consider the points $M$, $N$, $P$ and $Q$ on the edges $SA$, $SB$, $SC$ and $SD$, respectively, such that $MNPQ$ is also a parallelogram.
a) If $ABCD$ is a rhombus, prove that $MNPQ$ is also a rhombus.
b) If $ABCD$ is a rectangle, prove that $MNPQ$ is also a rectangle.
a) If $ABCD$ is a rhombus, prove that $MNPQ$ is also a rhombus.
b) If $ABCD$ is a rectangle, prove that $MNPQ$ is also a rectangle.