Page 109 - classs 6 a_Neat

B
INTERIOR AND EXTERIOR OF AN ANGLE Now, there are the following possibilities:
(i) If ray ED lies between ray BA and ray BC, as shown in the figure (i), we say that DEF is smaller than
ABC and we write, DEF < ABC.

O A A D

D A A
Let √AOB be a given angle. Then B

(i) All those points which lie inside the angle form the interior of the angle, R B (E) C (F) B (E) (ii) C (F) B (E) (iii) C (F)
(ii) All those points which lie outside the angle form the exterior of the angle, P (i)
(iii) Every point of each of the arms of the angle is said to lie on the angle. (ii) If ray ED lines beyond ray BA. as shown in the figure (ii), we say that DEF is larger than ABC and we
O Q A A write, DEF > LABC.
In the adjoining figure, the point Plies in the interior of √AOB, the point R lies in the exterior of AOB and the
points A, 0, B, Q all lie on AOB. (iii) If ray ED lines along ray BA, we say that DEF is congruent to ABC and we write, LDEF = ABC. See
the figure (iii) above.

MAGNITUDE OF AN ANGLE AND ITS MEASUREMENT UNITS OF MEASURING AN ANGLE
B The standard unit of measuring an angle is degree, to be denoted by o0•.
ANGLE AS ROTATION OF A RAY Suppose a ray after starting from its initial
position OA rotates about the point O and takes the final position OB. Then, Final position RIGHT ANGLE
we say that an angle √AOB has been described by the rotating ray with O as A quarter turn of a ray OA about O describes an angle called a right angle. B
vertex, and OA and OB as its arms. The measure of a right angle is 900•
O Initial position A In the adjoining figure, AOB = 90 •
0
MAGNITUDE OF AN ANGLE The magnitude of an angle is the amount of rotation through which one of the
arms must be rotated about the vertex to bring it to the position of the other. 1 right angle = 90". O (A right angle) P

COMPARING TWO ANGLES We say that l is greater than 2 if the magnitude of l is greater than that of 1° = 60 minutes, written as 60 '.
√2. Also, in other words, we say that 2 is smaller than √1 l° = 60 seconds, written as 60" .

VARIOUS TYPES OF ANGLES

1 2 (i) ACUTE ANGLE An angle whose measure is more than 0° but less than goo is called an acute angle . .
In the given figure, AOB is an acute angle.
(i) (ii) B

COMPARISON BY INSPECTION Clearly, the more is the opening between two arms, the greater will be the O
magnitude of an angle. So, sometimes we may compare two angles simply by looking at them. (Acute angle) A

In the figures (i) and (ii) given above, we can clearly say that l is greater than L2. (ii) RIGHT ANGLE An angle whose measure is 900 is called a right angle.
In the given figure, LOM = 900 = 1 right angle.
COMPARING ANGLES BY USING TRACING PAPER Suppose we have to compare two angles √ABC
and DEF. We place a tracing paper on one of the angles, say √DEF and copy this angle on the tracing paper.
Now, place the traced angle DEF on ABC such that the point E lies on the point Band the ray EF lies along M
the ray BC. A D

O
B C E F (A right angle) L