Every one of you knows to draw the geometrical shapes like squares, rectangles, triangles etc. But can you draw these same shapes without using the line segment? No!!! To draw these shapes, the line segment is the most important thing. Let us study the construction of the line segment.

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## Line Segment

The line is the combination of points which extends infinitely in both directions. But line segment is the part of the line with fixed endpoints.

## Construction

Suppose you are the given the length of the line segment as 6 cm. How do you draw it?

- Take a ruler and mark a 0 point at one end the other point at the given length that is at 6 cm.
- Join the two points and so you a line segment of length 6 cm.
- Name the two end of the line segment as A and B respectively.
- The other way to draw the line segment is using a ruler and a compass.
- Take a ruler and put the compass just above the ruler such that the pointed tip of the compass is at 0 and the pencil is at 6 cm.
- Now keep the compass at point A and make an arc at 6 cm at the point B
- So we get the required line segment.

### Drawing the Copy of the Line Segment

Suppose you are given a line segment of an unknown value and you are asked to draw the line segment of the same length. How do you do it?

- We make of a compass.
- Place the pointed tip of the compass is at one end and the pencil is at the other end.
- Now draw a line l and take a point say P anywhere on the line. Place the compass on the point P.
- Make an arc such that it cuts line at point Q. So the distance of this constructed line will be the same as that of the given line segment.

### Construct the Perpendicular to a line through a point on it

- Draw a line l with a ruler and mark a point P on the line.
- Take a compass and with P as the centre take a convenient radius from and make an equidistance arc on the line.
- Name intersecting points of the lines and arcs as Q and R.
- Now taking Qand R as the centres and the radius greater than QP construct two arcs. which cut each other at S.
- Mark intersecting point of arcs as S and Join S and P.

### Construct perpendicular to a line from a given point outside the line

- draw a line with the ruler and take a point A outside the line.
- From A draw equidistant arcs to cut the lines and now mark points as D and E.
- From D and E draw two equidistant arcs on the opposite side of the line.
- Now mark the intersecting point of two arcs as F and join the points A and F.

### Perpendicular Bisector

- Draw a line segment AB of any length.
- Now, take A as a centre and draw a circle using the compass. The radius of the circle should be more than half the length of AB.
- Now, take B as a centre and draw a circle with the same radius using the compass. Let it cut the previous circle at C and D.
- Join the points CD. It cuts AB at O as O is the midpoint of AB.
- Also, COA and COB are right angles and so CD is the perpendicular bisector of AB.

## Solved Examples For You

Q.1 To construct a line segment of a given length, which of the following pairs of instruments are needed?

- Ruler and Protractor
- Ruler and Compass
- Compass and Divider
- Protractor and Divider

Solution: B. Ruler and Compass are used to construct a line segment.

Q.2 If PQ is the perpendicular bisector of AB then PQ divides AB in the ratio:

- 1: 2
- 1: 3
- 2: 3
- 1: 1

Solution: D. The perpendicular bisector always divides the segment into 2 equal parts.

∴ PQ divides AB in the ratio 1: 1

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