Page 176 - ICSE Math 6

16 Constructions

Key Concepts

• Construction of Line Segments • Construction of Angles (60°, 120°, 90°, 30°, 45°, 135° )
• Construction of Perpendicular Bisectors of Line • Construction of Angle Equal to a Given Angle
Segments • Construction of Perpendicular to a Line
• Construction of Bisectors of Angles

Back in time, people didn’t have computers or other gadgets to draw accurate angles, lines, geometric
shapes, etc. They used to draw all of these by their hand with the help of some geometrical instrument
such as compass and ruler. In this chapter, we will learn to construct line segments, angles, perpendicular
bisectors, bisectors of angles, etc., using a ruler and a compass.

Construction of a Line Segment of given Length
Let’s draw the line segment of length 3.5 cm.

One way to draw the line segment is to mark a point A on the A B
ruler coinciding with 0 and the other point B coinciding with
3.5 mark. Join A and B to get the line segment of length 3.5 cm.

A better method using a ruler and a compass is given as follows.

Step 1: Draw a line l and mark a point A on it. A
l
Step 2: Place the pointed end of the compass at zero mark of the
ruler and open it to take the pencil end at 3.5 cm mark.

Step 3: Without changing the opening of the compass, place its
pointed end at A and draw an arc to cut the line l at B.
Thus, AB is the line segment of the required length. A 3.5 cm B l

The above method can also be used to draw a line segment of length equal to the length of the
given line segment.

Try These

1. Using a ruler, draw a 4 cm long line segment and then make its copy using a ruler and a compass.
2. Can you draw a line segment of length 3.56 cm, using a ruler? why?

To Draw a Perpendicular Bisector of a Line Segment

Let PQ be a line segment. If a line AB intersects PQ at O such A
that ∠AOQ = 90° and PO = OQ, then the line AB is known as the
perpendicular bisector of line segment PQ. P O Q
To draw a perpendicular bisector of a line segment, follow the
given steps. B

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