Question

Draw a line segment AB of length 5.3 cm. Using two different methods bisect AB.

Answer 1

Steps of Construction :

1. Draw a line segment AB = 5.3 cm

2. With A as centre and radius equal to more than half of AB, draw arcs on both sides of AB.

3. With B as centre and with the same radius as taken in step 2, draw arcs on both the sides of AB.

4. Let the arcs intersect each other at points P and Q.

5. Join P and Q.

6. The line PQ cuts the given line segment AB at point O.

Thus, PQ is a bisector of AB such that

$OA=OB=\frac{1}{2}AB$

Second Method

Steps of Construction :

1. Draw the given line segment AB = 5.3 cm.

2. At A, construct $\angle$PAB of any suitable measure. Then $\angle$PAB=${60}^{\circ }$ construct $\angle$QBA = ${60}^{\circ }$

3. From AP, cut AR of any suitable length and from BQ ; cut BS = AR.

4. Join R and S

5. Let RS cut the given line segment AB at the point O.

Thus RS is a bisector of AB such that OA = OB = $\frac{1}{2}AB$