Perpendicular Bisectors:
A perpendicular bisector is a line that divides a given line segment exactly into two halves forming 90 degrees angle at the intersection point.
Properties of a Perpendicular Bisector:
- It divides AB into two equal halves or bisects it.
- It makes right angles with (or is perpendicular to) AB.
- Every point in the perpendicular bisector is equidistant from points A and B.
While working with practical geometry, we will often find the application
of perpendicular bisectors; say when we are asked to draw an isosceles
triangle, or when we have to determine the centre of a circle, etc.
Below are the steps to construct a perpendicular bisector of a line
using a compass and a ruler.
Q.1. Draw a line segment AB of length 10 cm. Construct the perpendicular bisector of AB.
Solution:
Construction Steps:
1. Using a ruler, draw a line segment AB of length 10 cm.
2. Adjust the arms of the compasses so that the distance between the ends is more than half the length of AB, more than 5 cm. With A as centre, draw arc 1 above AB and draw arc 2 below AB.
3. Using the same radius as in Step 2, with B as centre, draw arc 3 to cut arc 1 at x and draw arc 4 to cut arc 2 at Y.
4. Join XY to cut AB at S.
Q.2. Draw an angle BAC of 66 degrees. Construct the angle bisector of SAC.
Solution:
Construction Steps:
1. Using a ruler and a protractor, draw an angle BAC of 66 degrees.
2. With A as centre and with a suitable fixed radius, draw an arc to cut AB at P and AC at Q.
3. With P as centre and with a suitable radius
4. using the same radius as in Step 3, with Q as centre, draw arc 2 to cut arc 1 at R.
5. Join AR.
