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a and b are parallel lines. They are cut by transversal c. Drag the blue points on c to move the transversal. How does this affect the angles formed by the intersection of a and b with c? Which angles are always congruent? Which angles are always supplementary?

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how to make perpendicular bisector (Steps)

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how to make perpendicular bisector (Steps)

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Construction of the Perpendicular Bisector of a Segment

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Construction of the Perpendicular Bisector of a Segment

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steps
a)make two points

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Graph functions, investigate equations, and plot data with our free graphing app

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NCERT Class VI Mathematics Chapter 14 Practical Geometry

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

Go to NCERT Class VI Mathematics Book Home Page All NCERT Books

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NCERT Class VI Mathematics Chapter 14 Practical Geometry

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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.

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Why did Euclid do it this way?

Why didn't Euclid just measure things with a ruler and calculate lengths?
For example, one of the basic constructions is bisecting a line (dividing it into two equal parts).
Why not just measure it with a ruler and divide by two?

One theory is the the Greeks could not easily do arithmetic.

They had only whole numbers, no zero, and no negative numbers.
This meant they could not for example divide 5 by 2 and get 2.5, because 2.5 is not a whole number - the only kind they had.
Also, their numbers did not use a positional system like ours, with units, tens , hundreds etc, but more like the Roman numerals. In short, it was quite difficult to do useful arithmetic.

So, faced with the problem of finding the midpoint of a line, it was very difficult to do the obvious - measure it and divide by two.
This led to the constructions using compass and straightedge or ruler.
It is also why the straightedge has no markings.
It is definitely not a graduated ruler, but simply a pencil guide for making straight lines.
Euclid and the Greeks solved problems graphically, by drawing shapes instead of using arithmetic.

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What's the point of Geometry? - Euclid explains it nice and easy!

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1. Students can identify and use the different geometrical instruments

2. To learn how to construct perpendicular lines through any given point. (point on the line or outside the line)

3. To learn how to how to bisect lines at right angles or to construct a perpendicular bisector

4.To learn how to construct angles using ruler and compass. (60˚, 120˚)

5. To learn how to bisect angles.

6.To apply the nowledge gained to construct (30˚, 90˚, 45˚ , 75˚, 105˚, 135˚)