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

RD Sharma Solutions Class 6 Chapter 15 Exercise 15.1

RD Sharma Class 6 Solutions Chapter 15 Ex 15.1 PDF Free Download

Exercise 15.1

Question 1

Identify parallel line segments:

i)

ii)

iii)

iv)

v)

vi)

Answers

  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

ADǁHGǁEFǁBC

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 \(\angle RBY\)