Table of contents  
Introduction  
Measuring Line Segment  
What are Angles?  
How to measure angles?  
What are Perpendicular Lines?  
Classification of Triangles  
What is a Quadrilateral?  
What is a Polygon? 
Here we see that line segment AB is longer than CD.
But we can’t tell how much longer so other methods were deduced.
Here, we have to compare AB and CD.
We will use tracing paper this time.
Trace line segment CD onto the paper and place it over the line segment on AB.
Now, we will be able to decide which is longer. This method depends on the accuracy in tracing the line segment.
But if we want to compare with another line segment you have to trace another line segment.
You cannot trace every time you want to compare.
So, yet another method was used.
Suppose the length is 5 cm, we may write,
Length AB = 5 cm or more simply as
AB = 5 cm.
Open the divider.
Place the endpoint of one of its arms at A and the endpoint of the second arm at B.
When two rays originate from a common point then the turn between two rays around the common point or vertex is called the angle between the two rays.
The two rays joining to form an angle are called arms of an angle and the point at which two rays meet to form an angle is called the vertex of the angle.
In the above figure, two rays and are the arm of an angle which meets at common initial point Q (vertex) and form an ∠PQR.
The measure of the angle PQR is written as ∠PQR but instead of writing this we can simply write it as ∠PQR.
Study the following positions:
You stand facing north.
By a ‘rightangleturn’ clockwise, you now face east.By another ‘rightangleturn’ you finally face south.
The last example was helpful to compare angles with a right angle. We classified the angles as acute, obtuse or reflex.
It cannot be useful if we have to 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 curved edge is divided into 180 equal parts. Each part is equal to a ‘degree’.
We call our measure, ‘degree measure’.
One complete revolution is divided into 360 equal parts. Each part is a degree.
Let us see how to measure the given angle using protractor.
Example:
Put the protractor over the angle and you will be get the accurate measure of angle.
Here, the measure of angle is 60°.
If a line AB is perpendicular to CD, we write AB ⊥ CD.
Triangles can be classified on the basis of
On the basis of side lengths, the triangles are classified into the following types:
Example: Draw a rough sketch of a quadrilateral PQRS.
Draw its diagonals.
Name them.
Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?
Answer:
The two diagonals are PR and QS.Diagonal PR and diagonal QS meet at point T which is in the interior of the quadrilateral PQRS.
We may classify polygons according to the number of their sides.
Let us see some of them:
Number of sides: 3
Name of polygon: Triangle
Illustration:
Number of sides: 4
Name of polygon: Quadrilateral
Illustration:
Number of sides: 5
Name of polygon: Pentagon
Illustration:
Number of sides: 6
Name of polygon: Hexagon
Illustration:
And the list goes on,
For 7 sides its heptagon
For 8 sides its octagon
For 9 sides its nonagon
For 10 sides its decagon...
134 videos326 docs42 tests

1. What is the importance of understanding elementary shapes in mathematics? 
2. How can measuring line segments help in reallife applications? 
3. What are some common examples of perpendicular lines in everyday life? 
4. How are triangles classified based on their angles and sides? 
5. Can you provide examples of threedimensional shapes commonly found in our environment? 

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