Pairs of Lines

Here we will learn pairs of lines.

When pairs of lines are given in a plane, they maybe

(i) parallel to each other.

(ii) intersecting each other.


(i) Parallel to each other:

Two lines in a same plane not intersecting each other are called parallel lines.

Parallel Lines

The lines AB and CD never meet each other at any point i.e., they are equidistant from each other at each and every point. Such A lines are called parallel lines.

Parallel lines AB and CD are represented as AB || CD.

Here symbol '||' is read as 'is parallel to'.


Note: The word 'in the same plane' should be carefully noted. There can be two lines in two different planes not parallel and at the same time, they do not meet each other.

Example:

1. Which of the following is a pair of parallel line segments or lines?

Pair of Parallel Line Segments

Solution:

Only (i) has a pair of parallel line segments.


(ii) Intersecting Lines:

Two lines that have only one point in common are called intersecting lines.

Intersecting Lines


If the angle between the intersecting lines is 90°, then the lines are perpendicular to each other. 

Perpendicular Lines

If AB is perpendicular to CD, it is represented as AB ⊥ CD or CD ⊥ AB.


Example:

1. Name the pairs of perpendicular lines in the following diagrams:

Pairs of Perpendicular Lines

Solution:

(i) From the figure, AB, BC;   AB, AD;   DC, AD;   DC, BC  are pairs of perpendicular lines

                i.e., AB ⊥ BC, AB ⊥ AD, DC ⊥ AD; DC ⊥ BC.


(ii) From the figure, ML ⊥ MN.


Math Questions and Answers on Pairs of Lines

1. Multiple Choice Questions (MCQ) on Pairs of Lines:

   Tick (the correct option.

(i) How many parallel lines are there in the capital letter 'E'?

(a) 4;     (b) 5;     (c) 6;     (d) 3


(ii) How many intersecting lines are there in the capital letter 'X'?

(a) 1;     (b) 2;     (c) 3;     (d) 4


Answer:

1. (i) (d) 3

(ii) (b) 2



2. Name the pairs of parallel line segments in the following diagrams.

Pairs of Parallel Line Segments

Answer:

2. (i) (SR || PQ), (SP || RQ)

(ii) (AB || ED), (BC || FE), (CD || AF) 

(iii) (AB || CD), (AC, BD)


3. Name the pairs of perpendicular line segments in the following diagrams.

Pairs of Perpendicular Line Segments

Answer:

3. (i) (DC ⊥ AD), (AD ⊥ AB)

(ii) There is no perpendicular line.


4. If lines ℓ || m  || n, what can you say about the lines ℓ and n?


Answer:

4. ℓ and n are also parallel since, ℓ || m and m  || n.

5. The adjoining figure represents a box.

Answer the following questions:

(i) Are the planes ABCD and ABEF parallel?

(ii) Name the plane parallel to CDGH.

(iii) Are the planes ADGF and BCHE parallel?


Parallel Planes

Answer:

5. (i) ABCD and ABEF are not parallel, they are perpendicular to each other.

(ii) The plane ABEF is parallel to CDGH.

(iii) Yes, the planes ADGF and BCHE are parallel.


6. In the figure, line segments AB and CD do not intersect each other.

Can you say that they are parallel?  Give reasons.

Parallel Lines or Not

Answer:

6. The line segments AB and CD are not parallel. If we extend both line segments, they will intersect each other. 




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