Question

If a point $Q$ lies between two points $P$ and $R$ such that $PQ=QR$, prove that $PQ=\frac{1}{2}PR$

Answer 1

$Q$ lies between $P$ and $R$

Thus $PR=PQ+QR$

Now, we are given $PQ=QR$

Put $QR=PQ$

$\Rightarrow PR=PQ+PQ$

$\Rightarrow PR=2PQ$

$\Rightarrow \frac{1}{2}PR=PQ$

$\Rightarrow PQ=\frac{1}{2}PR$

Hence proved.