# RD Sharma Solutions Class 6 Pair Of Lines And Transversal Exercise 15.1

## RD Sharma Solutions Class 6 Chapter 15 Exercise 15.1

#### Exercise 15.1

Question 1

Identify parallel line segments:

i)

ii)

iii)

iv)

v)

vi)

1. BC ǁ DE
2. AB ǁ DC , AD ǁ BC
3. AB ǁ DC , AD ǁ BC
4. PQ ǁ TS , UT ǁ QR , UP ǁ SR
5. AB ǁ DC ǁ EF , AD ǁ BC and DE ǁ CF
6. BC ǁ EF , 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

AHǁDGǁCFǁBE

ABǁDCǁGFǁHE

Question 3

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

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 dstance 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 – True

ii) Distance between two parallel lines is not same everywhere – False

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

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

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

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

vi) No two parallel segments intersect each other – True

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

viii) Two lines perpendicular to the same line are parallel – True

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

#### Exercise 15.2

Question 1

i) Alternate corresponding angles

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) Angles alternate to $\angle d$ and $\angle g$ and angles corresponding to angles $\angle f$and $\angle h$ in the figure

The alternate angle to $\angle d$ is $\angle e$ and alternate angles to $\angle g$ is $\angle b$

The corresponding angles to $\angle f$ is $\angle c$ and $\angle h$ is $\angle a$

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

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

So, the alternate angle of $\angle PQR$ is $\angle QRA$

The corresponding angle $\angle RQF$ and $\angle BRA$

The alternate angle of $\angle PQE$ is $\angle BRA$

iv) Interior angles on the same side of the transversal line ‘n’ are $\angle d$ and $\angle f$ , $\angle a$ and $\angle e$

Exterior angles on the same side of the transversal line ‘n’ are $\angle c$ and $\angle g$ , $\angle b$ and $\angle h$

Question 2

Match column A and column B .

i) Vertically opposite angles – c – $\angle PAB$ and $\angle XAQ$

ii) Alternate angles – a – $\angle PAB$ and $\angle ABS$

iii) Corresponding angles – b – $\angle PAB$ and $\angle RBY$