CAT Parallel and a Transversal Lines - Practice Questions & MCQ

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

Transversal: A straight line which cuts two or more straight lines at distinct points is called a transversal.

Line t intersects lines AB and CD at points E and F respectively. Therefore, line T is a transversal for lines AB and CD. Observe that four angles are formed at each of the points E and F.

Let us name these angles as ∠ 1, ∠ 2, . . ., ∠8 as shown in the above figure.

Angle formed when a transversal cuts two lines

∠ 1, ∠ 2, ∠ 7 and ∠ 8 are called exterior angles, while ∠ 3, ∠ 4, ∠ 5 and ∠ 6 are called interior angles.

Corresponding angles :

Alternate interior angles :

Alternate exterior angles:

Interior angles on the same side of the transversal:

Interior angles on the same side of the transversal are also referred to as consecutive interior angles or allied angles or co-interior angles.

Lines Parallel to the Same Line

Theorem 6 : Lines that are parallel to the same line are parallel to each other.

In other words, lf three lines are given, l, m and n and l is parallel to n, m is parallel to n. And we will see weather line l parallel to m or not. 

A transversal t, cutting l, m and n  at E, F, G respectively.

Since, l is parallel to n and transversal t cuts them at E and G respectively,

so,                    ∠1  = ∠3              [Corresponding angles]

Again, m is parallel to n and transversal t cuts them at f and G respectively,   

so,                    ∠2  = ∠3              [Corresponding angles]

therefore,         ∠2  = ∠3           

But these are corresponding angles formed when the transversal t cuts l and m at E and F respectively.

therefore l and m are parallel to each other by corresponding angle axiom.