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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.
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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.
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.
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
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.
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.
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
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
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.
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.
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.
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
The following figures are examples of the different types of angles.
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
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.
Polygons • Two-dimensional shapes that have sides made from straight lines.
Quadrilaterals • Any polygon shapes with four straight sides.
Rectangle 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. • A four sided two-dimensional shape with two pairs of parallel sides that meet at right angles.
Circle • A 2-dimensional shape made by drawing a curve that is always the same distance from a fixed point.
Square Triangle Two-dimensional shape with three straight sides and three angles. • Two dimensional shape with 4 sides of the same length and 4 90° angles.
Three dimensional shapes • These shapes are solid or hollow. • They have three dimensions – length, width and height.
Face • Part of a shape that is flat.(Or curved) • E.g. A cube has 6 of these.
Edge • The line where two faces meet. • E.g. A cube has 12 of these.
Vertices • The place where three or more edges meet. • This pyramid has 4 of these.
Cube • A three-dimensional shape which has 6 square faces all the same size.
Cuboid • A three-dimensional shape which has 6 rectangular faces or 2 square faces and 4 rectangle faces.
Sphere • A perfectly round three-dimensional shape, like a ball. It has only one curved face.
Hemisphere • A three-dimensional shape that is half a sphere.
