Lines and Angles Formula Class 9 PDF Free Download

Are you looking for important formulas of Lines and Angles for Class 9? You’re in the right place! In this post, we’ve compiled all essential formulas from Chapter 7 of Class 9 Maths – Lines and Angles. You can download the free PDF and revise quickly for your exams.

1. Angle : Two ray OA and OB having a common end point O from ∠AOB.

2. Interior of an Angle : The interior of an angle ∠AOB is the set of all points in its plane, which lie on the same side of OA as B and also on the same side of OB as A.

3. Exterior of an Angle : The exterior of an angle ∠AOB is the set of all those points in its plane , which do not lie on the angle or in its interior.

4. An angle of 360⁰ : If a ray OA starting from its original position OA , rotates about O in the anticlockwise direction and after making a complete revolution it come back to its original position.

5. Types of Angle :

(i). Right Angle : An angle whose measure 90⁰ is  called a right angle.

(ii). Acute Angle : An angle whose measure is more than 0⁰ but less than 90⁰ is called an acute angle.

(iii). Obtuse Angle : An angle whose measure is more than 90⁰ but less than 180⁰ is called an obtuse angle.

(iv). Straight Angle : An angle whose measure 180⁰ is called a straight angle.

 

(v). Reflex Angle : An angle whose measure is more than 180⁰ but less than 360⁰ is called reflex angle.

(vi). Complete Angle : An angle whose measure 360⁰ is called a complete angle.

6. Equal Angles : Two angles are said to be equal , if they have the same measure.

7. Complementary Angle : Two angle are said to be complementary , if the sum of their measures is 90^0.

8. Supplementary Angle : Two angle are said to be supplementary , if the sum of their measures is 180^0.

9. Adjacent Angles : Two angles are called adjacent angles if – 

10. Some Results on Angle Relations.

(i). If a ray stands on a line then the sum of the adjacent angles is 180^0.

(ii). The sum of all the angles fromed on the same side of a line at a point on the line is 180^0.

(iii). The sum of all the angles around a point is 360⁰

(iv). If the sum of two adjacent angles is 180⁰ then the non – common arms of the angles are in a straight line.

(v). Two angles are called a pair of vertically opposite angles , if their arms form two pairs of opposite rays.

(vi). If two lines intersect then the vertically opposite angles are equal.

11. Parallel Lines : If two lines lie in the same plane and do not intersect when produced on either side then such lines are said to be parallel to each other.

12. If a transversal cuts two parallel lines then each pair of corresponding angles are equal.

13. If a transversal intersects two parallel lines then alternate angles of each pair of interior angles are equal.

14. If a transversal intersects two parallel lines then each pair of consecutive interior angles are supplementary.

15. If a transversal intersects two lines making a pair of alternate interior angles equal, then the two lines are parallel.

16. If a transversal intersects two lines in such a way that a pair of consecutive interior angles are supplementary then the two lines are parallel.

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