CBSE Class 9 Maths Notes for Chapter 6 Lines and Angles

Line segment: A line segment is a line with two end points.

Ray: A part of the line with one end point is called a ray.

Collinear points: If three or more points lie on the same line, they are called collinear points

Non-collinear points: If three or more points do not lie on the same line they are said to be non-collinear.

Angle: An angle is formed when two rays originate from the same end point.

Arms: The arms of an angle are the rays that make the angle.

Vertex: The end point at which the rays making the angle meet is called the vertex.

 

TYPES OF ANGLE:

Acute angle: An angle measuring between 0^o and 90^o is an acute angle.

Right angle: An angle equal to 90^o is called a right angle.

Obtuse angle: An angle measuring greater than 90^obut less than 180^o is called an obtuse angle.

Reflex angle: An angle measuring greater than 180⁰ but less than 360⁰ is called a reflex angle.

Complementary angles: Two angles whose sum is 90^o are called complementary angles.

Supplementary angles: Two angles whose sum is 180^o are called supplementary angles.

 

AXIOMS AND THEOREMS

Linear pair axioms:

Axiom 1: If a ray stands on a line, then the sum of two adjacent angles so formed is 180^o.

Axiom 2: If the sum of two adjacent angles is 180^o, then the non-common arms of the angles form a line.

Corresponding angles axiom:

Axiom 3: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

Axiom 4: If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.

Theorems:

1. If two lines intersect each other, then the vertically opposite angles are equal.
2. If a transversal intersects two lines, then each pair of alternate interior angles is equal.
3. If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.
4. If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.
5. If a transversal intersects two lines such that a pair of interior angles are on the same side of the transversal is supplementary, then the two lines are parallel.
6. Lines which are parallel to the same line are parallel to each other.
7. The sum of the angles of a triangle is 180^o.
8. If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.