What are Transversal Line?
The line which intersects two distinct lines in a plane at two distinct points is called a transversal.
In the below figure, line 't' is transversal to lines l and m, intersecting these two lines at points A and B.
Also, we observe in the below figure, line 't' is not transversal line because it intersects line l and m at one point only.
Angles made by the transversal with two lines:
l and m are two lines in a plane. Transversal 't' intersects these two lines at points A and B. Eight angles are formed, i.e., ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, ∠8. The angles marked have their special names.
Angles whose arms include AB are called interior angles. In the given figure, ∠3, ∠4, ∠5, ∠6 are interior angles.
Angles whose arms do not include AB are called exterior angles. In the given figure ∠1, ∠2, ∠7, ∠8 are exterior angles.
Pair of corresponding angles:
These are pair of angles:
• Which lie on the same side of the transversal.
• If one is an interior angle, the other will be an exterior angle.
• They do not form a linear pair. In the figure, corresponding angles are: (∠2, ∠6); (∠3, ∠7); (∠1, ∠5); (∠4, ∠8)
Pair of alternate angles:
These are pairs of angles:
• Which lie on opposite sides of transversal.
• Both are either exterior angles or both are interior angles.
• They do not form a linear pair. In the given figure, alternate angles are:
(∠4, ∠6); (∠3, ∠5) these are interior alternate angles. In these pair of arms, arm AB is included.
(∠1, ∠7); (∠2, ∠8) these are exterior alternate angles. They do not include arm AB.
Pair of co-interior or conjoined or allied angles:
These are pairs of interior angles which lie on the same side on the transversal. In the given figure, co-interior angles are (∠3, ∠6); (∠4, ∠5)
Results when two parallel lines are cut by the transversal:
When parallel lines 'l' and 'in' are cut by the transversal line 't' then
• Pairs of corresponding angles are equal ∠2 = ∠6, ∠3 = ∠7, ∠1 = ∠5, ∠4 = ∠8
• Pairs of alternate angles are equal ∠4 = ∠6, ∠3 =∠5 , ∠ 1 = ∠7, ∠2 = ∠8
• Interior angles on the same side of transversal are supplementary ∠6 = 180°, ∠4 + ∠ 5 = 180°
When two lines are cut by a transversal and if
• pairs of corresponding angles are equal
• or pairs of alternate angles are equal
• or interior angles on the same side of transversal are supplementary. Then two lines are said to be parallel to each other.
● Lines and Angles