Page 42 - Ganit Kaushal

For instance, look at the given animals opening their mouths. Some mouths are open wider than others, the
more the jaw opens, the larger the angle!
Can you arrange these animals in the order of their open
jaw angles from smallest to largest?
Yes, you got it right, it’s –

Fish → Crocodile → Snake → Bird.

Comparing Angles by Superimposition

If the difference in the rotations among various angles is quite small, then there can be a viewing error. It is
difficult to observe angles just with the naked eye and decide which angle is larger and which is smaller. So,
we need precision to compare them.

Two angles can be compared by placing one over the other by using tracing paper, i.e., by superimposition.
While superimposing, the vertices and the initial rays of the angles must overlap, then the one whose final
ray lies after the other, in an anticlockwise sense, is the greater of the two (see figure below).

After superimposition, it becomes clear which angle is smaller and which is larger.
The following picture shows that the two angles are superimposed.

It clearly shows that ∠PQR is larger than ∠ABC.

P P
A A

B C Q R Q (B) R C
Two angles are said to be equal if, after superimposition, the vertex and the two rays of both angles overlap
each other.
In the figure below, it can be observed that ∠AOB = ∠XOY, as, after superimposition, the vertices of the two
angles and both the rays overlap exactly one on top of the other.

A X X
A

O B O Y O B Y
It can be observed that equal angles are obtained by an equal amount of rotation of the initial arm. Here, an
equal amount of rotation is needed to move arm OB to arm OA and arm OY to arm OX.

Remember

• ncreasing the length of the arms of an angle does not increase the size of the angle.
I
• The size of an angle is increased only by increasing the amount of rotation of the initial arm about the vertex.
• To name an angle, two points, one on each arm and the vertex are used, with the vertex always in the middle.
• The symbol ‘∠’ is used to denote an angle.

40 Mathematics-6