National Council of Educational Research and Training (NCERT) Book for Class VI

Subject: Mathematics

Chapter: Chapter 14 – Practical Geometry

Class VI NCERT Mathematics Text Book Chapter 14 Practical Geometry is given below.

**14.1 Introduction**

We see a number of shapes with which we are familiar. We also make a lot of pictures. These pictures include different shapes. We have learnt about some of these shapes in earlier chapters as well. Why don’t you list those shapes that you know about alongwith how they appear?

In this chapter we shall learn to make these shapes. In making these shapes we need to use some tools. We shall begin with listing these tools, describing them and looking at how they are used.

We are going to consider **“Ruler and compasses constructions”, using ruler, only to draw lines, and compasses,** only to draw arcs.

Be careful while doing these constructions.

Here are some tips to help you.

(a) Draw thin lines and mark points lightly.

(b) Maintain instruments with sharp tips and fine edges.

(c) Have two pencils in the box, one for insertion into the compasses and the other to draw lines or curves and mark points.

**14.2 The Circle**

Look at the wheel shown here. Every point on its boundary is at an equal distance from its centre. Can you mention a

few such objects and draw them? Think about five such objects which have this shape.

**14.3 A Line Segment**

Remember that a line segment is bounded by two end-points. This makes it possible to measure its length with a ruler.

If we know the length of a line segment, it becomes possible to represent it by a diagram. Let us see how we do this.

**EXERCISE 14.6**

1. Draw ∠POQof measure 75° and find its line of symmetry.

2. Draw an angle of measure 147° and construct its bisector.

3. Draw a right angle and construct its bisector.

4. Draw an angle of measure 153° and divide it into four equal parts.

5. Construct with ruler and compasses, angles of following measures:

(a) 60° (b) 30° (c) 90° (d) 120° (e) 45° (f) 135°

6. Draw an angle of measure 45° and bisect it.

7. Draw an angle of measure 135° and bisect it.

8. Draw an angle of 70o. Make a copy of it using only a straight edge and compasses.

9. Draw an angle of 40o. Copy its supplementary angle.

**What have we discussed ?**

This chapter deals with methods of drawing geometrical shapes.

1. We use the following mathematical instruments to construct shapes:

(i) A graduated ruler (ii) The compasses

(iii) The divider (iv) Set-squares (v) The protractor

2. Using the ruler and compasses, the following constructions can be made:

(i) A circle, when the length of its radius is known.

(ii) A line segment, if its length is given.

(iii) A copy of a line segment.

(iv) A perpendicular to a line through a point

(a) on the line (b) not on the line.

(v) The perpendicular bisector of a line segment of given length.

(vi) An angle of a given measure.

(vii) A copy of an angle.

(viii) The bisector of a given angle.

(ix) Some angles of special measures such as

(a) 90 Degree (b) 45 Degree (c) 60 Degree (d) 30 Degree (e) 120 Degree (f ) 135 Degree

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