2. Index
1. Introduction
2. Measuring line segments
2.1 Comparison by observations
2.2 Comparison by tracing
2.3 Comparison by ruler and divider
3. Angles
4.Shapes
4.1 Two dimensional
4.2 Three dimensional
3. Introduction
• All the shapes we see around us are formed using
curves or lines. We can see corners, edges, planes,
open curves and closed curves in our surroundings.
We organize them into line segments, angles,
triangles, polygons and circles. We find that they
have different sizes and measures.
4. Measuring line segments
• A line segment is a fixed portion of a line. This
makes it possible to measure a line segment. This
measure of each line segment is a unique number
called its “length”. We use this idea to compare line
segments.
• To compare any two line segments, we find a
relation between their lengths.
5. Comparison by observations
• By just looking at them can you tell which one is longer?
a b
• You can see that B is longer.
• But you cannot always be sure about your usual
judgment. For example, look at the adjoining segments :
a
b
• You cannot tell which is longer
6. • The difference in lengths between these two may not
be obvious. This makes other ways of comparing
necessary.
• In this adjacent figure, AB and PQ have the same
lengths. This is not quite obvious.
b
p q
a
• So, we need better methods of comparing line
segments.
7. Comparison by tracing
A B C D
•To compare AB and CD, we use a tracing paper, trace
CD and place the traced segment on AB.
•Can you decide now which one among AB and CD is
longer?
•The method depends upon the accuracy in tracing the
line segment. Moreover, if you want to compare with
another length, you have to trace another line segment.
This is difficult and you cannot trace the lengths
everytime you want to compare them.
8. Comparison using Ruler and a Divider
• Note how the ruler is marked along one of its edges.
It is divided into 15 parts. Each of these 15 parts is
of length 1cm. Each centimeter is divided into
10subparts. Each subpart of the division of a cm is
1mm
9. • Since 1cm = 10 mm, we will write
2cm and
3mm as 2.3
7.7 mm as
7cm 7mm
Place the zero mark of the ruler at A. Read the mark
against B. This gives the length of AB. Suppose the
length is 5.8 cm, we may write,
Length AB = 5.8 cm or more simply as AB = 5.8 cm.
A B
10. • When you are working with a ruler, some errors might
creep into your observations without you noticing it. The
positioning of your eye while reading the observation is
very important, especially, while using a thick ruler.
• See the figure given.
• When you are marking the length of the line segment, the
eye should be directly above the mark on the ruler. In the
above figure, the position of the eye in the middle shows
the correct way of taking the reading. The positions of the
eye on the left and right lead to wrong observations. These
errors are called positioning errors or parallax errors.
11. • Using divider for measurement.
• Place the two end points of the arms of a divider at
the two end points of the line segment to be
measured.
12. • Then, without disturbing the divider, place it on the
ruler with one of its arms at the 0 mark of the ruler.
• Now, the measurement of the two arms of the
divider is the measurement of the length of the line
segment.
13. Angles
• Consider a notebook and look at the angle made by
the adjacent sides.
• The adjacent sides OB and OA of the notebook
form an angle AOB. This angle is a right angle
15. • The following figures are examples of the different
types of angles.
16. Shapes
• It is an enclosed space, the boundaries of which are
defined by other elements like lines, colours, values,
textures, etc.
• There are two types of shapes :
two dimensional
three
dimensional
17. Two dimensional shapes
• These shapes are flat and can only be drawn on
paper.
• They have two dimensions – length and width.
• They are sometimes called plane shapes.
20. Rectangle
• A four sided two-
dimensional shape with
two pairs of parallel sides
that meet at right angles.
Rhombus
• A 4-sided flat shape with
straight sides where all
sides have equal
length. Also opposite sides
are parallel and opposite
angles are equal.
21. Circle
• A 2-dimensional shape made by drawing a curve
that is always the same distance from a fixed point.
22. Square
• Two dimensional shape
with 4 sides of the same
length and 4 90° angles.
Triangle
• Two-dimensional shape
with three straight sides
and three angles.
23. Three dimensional shapes
• These shapes are solid or hollow.
• They have three dimensions – length, width and
height.
24. Face
• Part of a shape that is flat.(Or curved)
• E.g. A cube has 6 of these.
25. Edge
• The line where two faces meet.
• E.g. A cube has 12 of these.
26. Vertices
• The place where three or more edges meet.
• This pyramid has 4 of these.
