06.05 Maths
Ch. 05. Understanding Elementary Shap
* Measuring Line Segments
A line segment is a fixed measured portion of a line. The measure of each line segment is a unique number, which is called its “length”.
Idea of this fixed measure makes, possiblties to measure a line segment. We find a relation between their lengths to compare any two line segments.
This can be done in several ways.
(i) Comparison by observation
Comparison by observation is not always sure because our usual judgment have more chances of errors due to improper viewings.
(ii) Comparison by Tracing
To compare AB and CD, we use a tracing paper.
Trace any one line and place the traced segment on other line. This method depends upon the accuracy in tracing the line segment.
To compare more length, we have to trace another line segment, which is difficult to trace the lengths everytime.
(iii) Comparison using Ruler and a Divider
We know that the ruler is marked along its edges which is divided into 15 parts.
Each of these 15 parts is of length 1cm. Each centimetre is divided into 10subparts. Each subpart of the division of a cm is 1mm.
To get correct measure, the eye should be correctly positioned, just vertically above the mark. Otherwise errors can happen due to angular viewing.
Measuring by divider is better way to avoid the above problem so use divider to measure length.
Open the divider. Place the end point of one of its arms at A and the end point of the second arm at B. Taking care that opening of the divider is not disturbed, lift the divider and place it on the ruler. Ensure that one end point is at the zero mark of the ruler. Now read the mark against the other end point.
Angles
Acute Angle
Right Angle
Obtuse Angle
Straight Angle
Reflex Angle
Complete Angle
There are four main directions. They are East (E), West (W), North (N) and South (S). We know that the Sun rises in the East and sets in the West.
There is a right angle between two regular sides.
NE, EN, ES, SE, SW, WS, NW, WN
There is a straight angle between two opposite direction.
NS, SN
We can also find the directions with the help of watch.
Measuring Angles
The improvised ‘Right-angle tester’ we made is helpful to compare angles with a right angle. We were able to classify the angles as acute, obtuse or reflex.
But this does not give a precise comparison. It cannot find which one among the two obtuse angles is greater. So in order to be more precise in comparison, we need to ‘measure’ the angles. We can do it with a ‘protractor’.
The measure of angle We call our measure, ‘degree measure’. One complete revolution is divided into 360 equal parts. Each part is a degree. We write 360° to say ‘three hundred sixty degrees’.
Think, discuss and write How many degrees are there in half a revolution? In one right angle? In one straight angle?
How many right angles make 180°? 360°?
N is shown by 12, East by 3, South by 6 and West by 9.
Measuring Angles
The improvised ‘Right-angle tester’ we made is helpful to compare angles
with a right angle. We were able to classify the angles as acute, obtuse or
reflex.
But this does not give a precise comparison. It cannot find which one among
the two obtuse angles is greater. So in order to be more precise in comparison,
we need to ‘measure’ the angles. We can do it with a ‘protractor’.
The measure of angle
We call our measure, ‘degree measure’. One complete revolution is divided
into 360 equal parts. Each part is a degree. We write 360° to say ‘three hundred
sixty degrees’.
Think, discuss and write
How many degrees are there in half a revolution? In one right angle? In one
straight angle?
How many right angles make 180°? 360°?
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