### Theorem 6.3 Class 9 If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.

Theorem 6.3 Class 9 If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel. Theorem 6.3 Class 9

## Class 9 Maths Chapter 6 Theorems Lines and Angles

- Theorem 6.1 If two lines intersect each other, then the vertically opposite angles are equal.
- Theorem 6.2 Class 9 If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.
- Theorem 6.3 Class 9 If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.
- Theorem 6.4 Class 9 If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.
- Theorem 6.5 Class 9 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.
- Theorem 6.6 Class 9 Lines which are parallel to the same line are parallel to each other.
- Theorem 6.7 Class 9 The sum of the angles of a triangle is 180º.
- Theorem 6.8 Class 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.