Question

Draw a line segment PQ = 8cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meet PQ at point R. Measure the lengths 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 ∠POR = 90°.

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 = 4cm, QR = 4 cm Since PR = QR, both are 4cm each

∴ PR = QR.