CBSE Class 9 Mathematics Lines And Angles Notes

CBSE Class 9 Concepts for Lines and Angles. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

Chapter- 6

Lines and Angles

Chapter Notes

Top Definitions

1. A line segment is a part of a line which has two end points.

2. A ray is a part of a line which has only one end point.

3. A line is a breadth less length which has no end point.

4. Three or more points when lie on the same line are called collinear points.

5. Three or more points when don’t lie on a straight line are called non collinear points.

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

7. The rays making an angle are called the arms of the angle.

8. The end point from the two rays forming the angle originate is called the vertex of the angle.

9. Two angles whose sum is 90° are called complementary angles.

10. Two angles whose sum is 180° are called supplementary angles.

11. Two angles are adjacent, if they have a common vertex, a common arm and their non–common arms are on different sides of the common arm.

12. If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and vice – verse. This property is called as the linear pair axiom.

13. The vertically opposite angles formed when two lines intersect each other. There are two pairs of vertically opposite angles.

14. A line which intersects two or more lines at distinct points is called a transversal.

a. Corresponding angles:

(i) Ð1 and Ð5 (ii) Ð2 and Ð6

(iii) Ð4 and Ð8 (iv) Ð3 and Ð7

b. Alternate interior angles:

(i) Ð4 and Ð6 (ii) Ð3 and Ð5

c. Alternate exterior angles:

(i) Ð1 and Ð7 (ii) Ð2 and Ð8

d. Interior angles on the same side of the transversal:

(i) Ð4 and Ð5 (ii) Ð3 and Ð6

Top Concepts

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

2. If the sum of two adjacent angles is 180°, then the non – common arms of the angles form a line.

3. If two lines intersect each other, then the vertically opposite angles are equal.

4. If a transversal intersects two parallel lines, then

a. Each pair of corresponding angles is equal.

b. Each pair of alternate interior angles is equal.

c. 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 on the same side of the transversal is supplementary, then the two lines are parallel.

6. If two lines are parallel to the same line, will they be parallel to each other.

7. Lines which are parallel to the same line are parallel to each other.

8. The sum of the angles of a triangle is 180°.

9. 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.

10. In exterior angle of a triangle is greater then either of its interior opposite angles.

11. If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

Top Diagrams

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