Two Parallel Lines Cut by a Transversal

Introduction to two parallel lines cut by a transversal:

Parallel lines:

Two lines on a plane that never  intersect or meet is known as parallel lines. The distance between both the lines must be the same. And they must not intercept with each other. It can also be explained as the length between parallel lines will be exactly same at any point. Examples of parallel lines are railway track, etc.

Transversal:

A straight line is said to be transversal if the line cuts two or more parallel lines at different points. In the figure the line l cuts the parallel lines a and b. So the line l is called as a transversal line

Two Parallel Lines Cut by a Transversal:

When two parallel lines are cut by a transversal then

The corresponding angles are equal

Pair of Vertically Opposite angles is equal

Pairs of Alternate interior angles are equal

Interior angles on same side are supplementary

Conditions Satisfies when Two Parallel Lines Cut by a Transversal:

The corresponding angles formed by the transversal will be equal. For example angle 4 and angle 6 are corresponding angles, and the other pairs of corresponding angles are (5 and 3), (8 and 2) and (1 and 7).

Therefore we have:               angle 6 = angle 4

angle 5 = angle 3

angle 8 = angle 2

angle 7 = angle 1

Pair of Vertically Opposite angles is equal

The pair of vertically opposite angles is equal when a transversal line is formed. For example, angle 1 and angle 3 are vertically opposite angles and the other pairs of vertically opposite angles are (2 and 4), (5 and 7) and (6 and 8).

Therefore we have:                angle 1 = angle 3

angle 2 = angle 4

angle 5 = angle 7

angle 6 = angle 8

Pairs of Alternate interior angles are equal

The pair of alternate angles is equal when the transversal line is formed. Here the pairs (2 and 6) and (3 and 7) are alternate interior angles. I have recently faced lot of problem while learning simple math problems for kids, But thank to online resources of math which helped me to learn myself easily on net.

Therefore we have:                angle 2 = angle 6

angle 3 = angle 7

Interior angles on same side are supplementary

Interior angles on same side are supplementary when a transversal is formed. The angles on the same side of the transversal are (6 and 3) and (2 and 7).

Therefore we have:                angle 3+ angle 6 = 180

angle 2 + angle 7 = 180