1. Properties of parallel lines cut by a transversal

2. Introduction When two parallel lines are cut by a transversal,
Transversal Lines
Parallel lines
When two parallel lines are cut by a
transversal,
Each pair of interior alternate angles are equal
Each pair of exterior alternate angles are equal
Each pair of corresponding angles are equal
Each pair of interior angles on the same side of the transversal are
supplementary (i.e 180°)
Let us see each rule one by one

3. Each pair of corresponding angles are equal
Rule 1
Each pair of corresponding angles are equal 2 1 6 5
∠2 = ∠6
∠1 = ∠5 4 3 8 7
∠4 = ∠8
∠3 = ∠7

4. Each pair of interior alternate angles are equal
Rule 2
Each pair of interior alternate angles are equal 3 4 5 6
∠3= ∠5
∠4 = ∠6

5. Each pair of exterior alternate angles are equal
Rule 3
Each pair of exterior alternate angles are equal 1 2 8 7
∠2= ∠8
∠1 = ∠7

6. Rule 4 Each pair of interior angles on the same side of the
transversal are supplementary (i.e 180°) 4 3 5 6
∠4 + ∠5 = 180°
∠3 + ∠6 = 180°

7. Rule 5
Each pair of exterior angles on the same side of the transversal are supplementary (i.e 180°) 1 2 7 8
∠2 + ∠7 = 180°
∠1 + ∠8 = 180°

8. Each pair of vertically opposite angles are equal2 1 4 3
∠2 = ∠4
∠1 = ∠3 5 6 7 8
∠5 = ∠7
∠6 = ∠8

9. Sum of pair of adjacent supplementary angles are supplementary (i
Sum of pair of adjacent supplementary angles are supplementary (i.e 1800) 1 2 3 2 3 4 1 4
∠1 + ∠2 = 180
∠2 + ∠3 = 180
∠3 + ∠4 = 180
∠1 + ∠4 = 180 5 6 7 6 7 8 5 8
∠5 + ∠6 = 180
∠6 + ∠7 = 180
∠7 + ∠8 = 180
∠5 + ∠8 = 180

10. Pair of angles are equal Sum of pair of angles are 1800
Properties of parallel lines cut by a transversal 3 5 2 1 4 6 7 8
Pair of angles are equal
Sum of pair of angles are 1800
Each pair of corresponding angles
are equal
Each pair of interior angles on the same side of the transversal are supplementary
(i.e 1800)
Each pair of interior alternate angles
are equal
Each pair of exterior angles on the same side of the transversal are supplementary
(i.e 1800)
Each pair of exterior alternate angles
are equal
Sum of pair of adjacent supplementary angles are supplementary
(i.e 1800)
Each pair of vertically opposite angles
are equal

11. l || m Example 1: Solution: Lines l || m, t is a transversal, ∠x?
Given:
l || m
t is a transversal
To find: ∠x
∠70° and ∠x are the pair of interior alternate angles
Ans: ∠ x = 70°
Rule2: Each pair of interior alternate
angles are equal

12. Example 2: Solution: Lines l || m, t is a transversal, ∠z? Given:
To find: ∠z
98° and ∠ z are the pair of interior angles lying on the same side of the transversal.
98° + ∠ z = 180°
98° + ∠ z - 98° = 180° - 98° (Subtract 98° from both sides of the equation)
∠ z = 82°
Rule4: Each pair of interior angles on the same side
of the transversal are supplementary (i.e 180°)

13. Rule1: Each pair of corresponding
Example 3:
Lines l || m, t is a transversal, ∠x?
Solution:
Given:
l || m
t is a transversal
To find: ∠x
∠140° and ∠ x are the pair of corresponding angles
∠x = 140°
Rule1: Each pair of corresponding
angles are equal

14. Example 4:
l 1, l2 be two lines and t is a transversal. Is ∠a = ∠b?
Solution:
Given:
l1, l2 be two lines
t is a transversal
To show: ∠a = ∠b
We know that when a parallel line cut by a transversal, each pair of alternate angles are equal.
But l1 and l2 are not parallel lines, so none of the properties holds good.
Therefore, ∠a ≠ ∠b

15. Try These Lines l || m, t is a transversal, ∠x?
2. Lines l || m, t is a transversal, ∠h?