In the figure, $ABCD$ and $PQRC$ are rectangles and $Q$ is the mid-point of $AC$.
Prove that $PR = \frac{1}{2}AC$.
"
Given:
$ABCD$ and $PQRC$ are rectangles and $Q$ is the mid-point of $AC$.
To do:
We have to prove that $PR = \frac{1}{2}AC$.
Solution:
$PR$ and $QC$ are the diagonals of rectangle $PQRC$.
This implies,
$PR = QC$
$Q$ is the mid-point of $AC$
This implies,
$QC = \frac{1}{2}AC$
Therefore,
$PR = \frac{1}{2}AC$
Hence proved.
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