Chapter 15: Pair of Lines and Transversal Exercise 15.1

Question: 1

Identify parallel line segments:

Parallel line Parallel line(ii) Parallel line(iii)
(i) (ii) (iii)
Parallel line(iv) Parallel line(v) Parallel line(ivi)
(iv) (v) (vi)


(i) BC ǁ DE

(ii) AB ǁ DC, AD ǁ BC

(iii) AB ǁ DC, AD ǁ BC

(iv) PQ ǁ TS, UT ǁ QR , UP ǁ SR

(v) AB ǁ DC ǁ EF, AD ǁ BC and DE ǁ CF

(vi) BC ǁ E, AB ǁ DF and AC ǁ DE


Question: 2

Name the pairs of all possible parallel edges of the pencil box whose figure is shown in the figure

Pairs of all possible parallel edges


(i) AH ǁ DG ǁ CF ǁ BE

(ii) AB ǁ DC ǁ GF ǁ HE

(iii) AD ǁ HG ǁ EF ǁ BC


Question: 3

In the figure, do the segments AB and CD intersect? Are they parallel? Give reasons.

Segments AB and CD intersect


In the given position, segments AB and CD do not intersect, but hey can if extended to a point. No, they are not parallel, as the distance between them is not constant.


Question: 4

State which of the following are true or false:

i) If two lines in the same plane do not intersect, then they must be parallel

ii) Distance between two parallel lines is not same everywhere

iii) If m perpendicular l and n perpendicular l and m ≠ n, then m parallel to n 

iv) Two non – intersecting co –planar rays are parallel 

iv) If Ray AB parallel to m, then line segment AB parallel to m 

v) If Ray AB parallel to m, then line segment AB parallel to m 

vi) No two parallel segments intersect each other 

vii) Every pair of lines is a pair of co-planar lines

viii) Two lines perpendicular to the same line are parallel

ix) A line perpendicular to one of two parallel lines is perpendicular to each other


State which of the following are true or false:

i) True

ii) False

iii) True

iv) False

iv) True

v) True

vi) True

vii) False

viii) True

ix) True


Question: 5

i) Alternate corresponding angles

Alternate corresponding angles

ii) Angles alternate to ∠d and ∠g and angles corresponding to angles ∠f and ∠h in the figure

Angles alternate

iii) Angles alternative to ∠PQR, angle corresponding to ∠RQF and angle alternative to ∠PQE in the figure



Alternate interior angles are:

Angle BGH and angle CHG

Angle AGH and angle CHF

Alternate exterior angles:

Angle AGE and angle DHF

Angle EGB and angle CHF

Corresponding angles are:

Angle EGB and angle GHD

Angle EGA and angle GHC

Angle BGH and angle DHF

Angle AGF and angle CHF


The alternate angle to ∠d is ∠e and alternate angles to ∠g is ∠b

The corresponding angles to ∠f is ∠c and ∠h is ∠a


In the given figure. ‘I’ is a transversal to ‘m’ and ‘n’

So, the alternate angle of ∠PQR is ∠QRA

The corresponding angle ∠RQF and ∠BRA

The alternate angle of ∠PQE is ∠BRA


Question: 6

Match column A and column B.

i) Vertically opposite angles → a. ∠PAB and ∠ABS

ii) Alternate angles → b – ∠PAB and ∠RBY

iii) Corresponding angles → c. ∠PAB and ∠XAQ


i) Vertically opposite angles → c. ∠PAB and ∠XAQ

ii) Alternate angles →  a. ∠PAB and ∠ABS

iii) Corresponding angles → b – ∠PAB and ∠RBY


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