Question

Draw a line segment PQ= 8 cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meets PQ at point R. Measure the length of PR and QR. Is PR=QR?

Answer 1

Steps of Construction :

$1.$ With $P$ and $Q$ as centers, draw arcs on both sides of $PQ$ with equal radii. The radius should be more than half the length of $PQ$.

$2.$ Let these arcs cut each other at points $R$ and $RS$

$3.$ Join $RS$ which cuts $PQ$ at $D$. Then $RS=PQ$. Also $\angle POR={90}^{\circ }$.

Hence, the line segment $RS$ is the perpendicular bisector of $PQ$ as it bisects $PQ$ at $P$ and is also perpendicular to $PQ$. On measuring the lengths of $PR=4$cm, $QR=4$ cm Since $PR=QR$, both are $4$cm each

$\therefore PR=QR$.