Facts that Matter
BASIC TERMS AND DEFINITIONS
Recall that a point is an exact location. We denote a point by a capital letter such as A, B, C, P and Q etc. The straight path between two points A and B is called a line segment AB. We denote it as. It has a definite length. A line segment when extended indefinitely in one direction is called a ray AB. It is denoted byhas one end-point A. A line segment when extendedindefinitely in both the directions is called a line AB. It is denoted by. It has no definite length and it is labelled by small letters ℓ, m, n, p, q, etc.
If three or more points lie on the same line they are called collinear points otherwise they are called non-collinear points.
An angle is formed when two rays originate from the same end-point. The rays making the angle are called arms of the angle and the end point is called the vertex of the angle.
Types of Angles
(i) An acute angle measures between 0º and 90º.
(ii) An angle which is exactly equal to 90º is called a right angle.
(iii) An angle greater than 90º but less than 180º is called an obtuse angle.
(iv) An angle which is exactly equal to 180º is called a straight angle.
(v) An angle which is greater than 180º and less than 360º is called a reflex angle.
(vi) An angle which is exactly equal to 360º is called a complete angle.
If the sum of two angles is 90º then they are called complementary angles whereas if the sum of two angles is 180º then they are called the supplementary angles.
PAIRS OF ANGLES [HAVING COMMON VERTEX]
(i) Adjacent Angles
Two angles are said to be adjacent angles, if
(i) They have the same vertex
(ii) They have a common arm.
(iii) Their non-common arms are on either side of the common arm.
In the figure, ∠BOA and ∠COB are adjacent angles.
(ii) Linear Pair of Angles
Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two opposite rays. In the figure ∠AOC and ∠BOC form a linear pair of angles.
If the sum of two adjacent angles is 180º, then the non-common arms of the angles form a straight line.
(iii) Vertically Opposite Angles
When two lines intersect each other at a point then they form two pairs of vertically opposite angles. In the figure AB and CD intersect at O and form ∠AOD and ∠BOC one pair of vertically opposite angles whereas ∠AOC and ∠BOD is the other pair.
The vertically opposite angles are always equal.