Question

In the adjacent figure $ABCD$ is a parallelogram $P,Q$ are the midpoints of sides $AB$ and $DC$ respectively. Show that $PBCQ$ is also a parallelogram

Answer 1

Since $AB\parallel CD$ [ Opposite sides of ${\parallel }^{gm}$ are parallel ]

$\Rightarrow PB\parallel QC$ [ Parts of parallel lines are parallel ]

Also, $AB=CD$ [ Opposite sides of ${\parallel }^{gm}$ are equal ]

$\Rightarrow \frac{1}{2}AB=\frac{1}{2}CD$

$\Rightarrow PB=QC$ [ P is the mid point of Ab and Q is the mid point of DC ]

Since $PB\parallel QC$ and $PB=QC$

One pair of opposite sides of $PBCQ$ are equal and parallel.

$\therefore PBCQ$ is a ${\parallel }^{gm}.$

Hence, the answer is solved.