lines and angles self learning material maths class 9

1. KOMAL RANAWAT
14162099
B.ED
SELF
LEARNING
MATERIAL
April 5
2015
LINES AND
ANGLES

2. LINES AND ANGLES
Basic Terms and Definitions
 Line
A line is a collection of points along a straight path. A line extends in both the
directions and has no endpoints. It has no definite length.
 Line segment
A line segment is a part of a line with two end points. There is only one line
segment joining two given points.
 Ray
A part of line with one end point is called a ray.
 Collinear points
All the points that lie on the same line are called collinear points.
 Angle
Two rays originating from the same end point form an angle.
Consider the two rays AB and AC originating from the same point A form an angle
named as ∠BAC or ∠CAB or ∠A. The rays that form the angle are called the arms
of the angle. The end point is called the vertex of the angle. The size of an angle is
measured in degrees.

3. Types of angles
 Acute angle
Angles measuring less than 90° but more than 0° are called acute angles.
 Right angle
An angle measuring 90° is called a right angle. A right angle is formed by the
intersection of two perpendicular lines.
 Obtuse angle
Angles measuring greater than 90° but less than 180° are called obtuse angles.

4.  Straight angle
An angle measuring 180° is called a straight angle.
 Reflex angle
Angles measuring greater than 180° but less than 360° are called reflex angles.
 Adjacent angles
Two angles are said to be adjacent if they have a common arm and a common
vertex.
 Linear pair of angles
Two adjacent angles are said to form a linear pair if their sum is 180°. Non-
common arms of the linear pair of angles form a straight line
 Vertically opposite angles
When two lines intersect, four angles are formed. The angles that are opposite to
each other are called vertically opposite angles. There are two pairs of vertically
opposite angles.
 Complementary angles
Two angles are said to be complementary, if their sum is 90°.
 Supplementary angles
Two angles are said to be supplementary if their sum is 180°.
Complementary and supplementary angles may or may not be adjacent angles.

5. Intersecting lines
Two or more lines that meet at one point are called intersecting lines. When two
lines intersect each other, then the vertically opposite angles are equal. Sum of all
the angles formed at a point is 360°.
Parallel lines
Lines on the same plane that never intersect are called parallel lines.
Transversal
A line that intersects two or more lines, at different points is called a transversal.
When a transversal intersects two lines, m and n, eight angles are formed, four
angles at each point, P and Q respectively. These angles are identified by their
positions.

6. • ∠1, ∠2, ∠7 and ∠8 are called exterior angles
• ∠3, ∠4, ∠5 and ∠6 are called interior angles
• ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8, ∠3 and ∠7 are pairs of corresponding
angles
• ∠1 and ∠7, ∠2 and ∠8 are pairs of alternate exterior angles
• ∠4 and ∠6, ∠3 and ∠5 are pairs of alternate interior angles
• ∠4 and ∠5, ∠3 and ∠6 are consecutive interior angles on the same side of
the transversal

7. If a transversal intersects two parallel lines, then
• each pair of corresponding angles is equal.
• each pair of alternate interior angles is equal.
• each pair of interior angles on the same side of the transversal is
supplementary
Two lines intersected by a transversal are parallel if, either
• any one pair of corresponding angles is equal, or
• any one pair of alternate interior angles is equal, or
• any one pair of interior angles on the same side of the transversal is
supplementary
Lines which are parallel to the same line are parallel to each other.
The sum of three angles of a triangle is 180°.
If a side of a triangle is produced, the exterior angle so formed is equal to the sum
of the two interior opposite angles.
QUESTIONS
Q1. Prove that if two lines intersect ,then both pairs of
vertically opposite angles are equal.
Q2. AB parallel to CD and EF parallel to DQ determine angle
PDQ , angle AED and angle DEF.

8. Q3. An exterior angle of a triangle is 105° and its interior
opposite angles are equal. Each of these equal angles
is________.
Q4. 3 angles of a triangle are a, b & c. if c = a+b/2, then find
value of 'c'