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CAT Parallel and a Transversal Lines - Practice Questions & MCQ

Edited By admin | Updated on Oct 04, 2023 04:20 PM | #CAT

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  • 4 Questions around this concept.

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In the figure below, m is a transversal.

 

 

Concepts Covered - 1

Parallel and a Transversal Lines

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 :

(i) ∠ 1 and ∠ 5
(ii) ∠ 2 and ∠ 6
(iii) ∠ 4 and ∠ 8
(iv) ∠ 3 and ∠ 7

 

Alternate interior angles :

(i) ∠ 4 and ∠ 6
(ii) ∠ 3 and ∠ 5

 

Alternate exterior angles:

(i) ∠ 1 and ∠ 7
(ii) ∠ 2 and ∠ 8

 

Interior angles on the same side of the transversal:

(i) ∠ 4 and ∠ 5
(ii) ∠ 3 and ∠ 6

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 at E and F respectively.

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

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