Chapter 15: Pair of Lines and Transversal Exercise 15.1

Question: 1

Identify parallel line segments:

(i)	(ii)	(iii)
(iv)	(v)	(vi)

Solution:

(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

Solution:

(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.

Solution:

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

Solution:

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

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

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

Solution:

i)

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

ii) 

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

iii)

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

Solution:

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

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

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