Basics of Geometry

Angles: When two straight lines meet at a point they form an angle. In the figure, the angle is represented as ∠AOB. OA and OB are the arms of ∠AOB. Point O is the vertex of ∠AOB. The amount of turning from one arm (OA) to other (OB) is called the measure of the angle (AOB).

Right angle: An angle whose measure is 90^o is called a right angle. ∠ BOA is a right angle in the figure.

Acute angle: An angle whose measure is less then one right angle (i.e., less than 90^o), is called an acute angle.

Obtuse angle: An angle whose measure is more than one right angle i. e. 90^o and less than two right angles

(i.e., less than 180^o and more than 90^o) is called an obtuse angle.

Reflex angle: An angle whose measure is more than 180^o and less than 360^o is called a reflex angle.

Complementary angles: If the sum of the two angles is one right angle (i.e., 90^o), they are called complementary angles. Therefore, the complement of an angle θ is equal to 90° − θ. ∠AOC & ∠ COB are Complementary angles.

Supplementary angles: Two angles are said to be supplementary, if the sum of their measures is 180^o. Here ∠BOC & ∠ COA are   Supplementary angles.

Example:   Angles measuring 130o and 50o are supplementary angles. Two supplementary angles are the supplement of each other. Therefore, the supplement of an angle θ is equal to 180° − θ.

·  The sum of all the angles round a point is equal to 360°.

·    If two lines intersect, then the vertically opposite angles are equal.

Angle a = angle b (vertically opposite angle)

·                     If a transversal  intersects two parallel lines, then each pair of corresponding angles are equal.

·                     Other facts :

1.  Linear pair :

a + b = 180°  

2.   Vertical opposite angles:

a = c & b = d e = g & f = h

3.   Alternate angles:

c = e, d = f

4.     Sum of Interior angle is always 180°:

c + f = d + e = 180°

Bisector of an angle: If a ray or a straight line passing through the vertex of that angle, divides the angle into two angles of equal measurement, then that line is known as the Bisector of that angle.

A point on an angle is equidistant from both the arms.

In the figure, Q and R are the feet of perpendiculars drawn from P to OB and OA. It follows that

PQ = PR.