RS Aggrawal 2020 2021 Solutions for Class 6 Maths Chapter 12 Parallel Lines are provided here with simple step-by-step explanations. These solutions for Parallel Lines are extremely popular among class 6 students for Maths Parallel Lines Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RS Aggrawal 2020 2021 Book of class 6 Maths Chapter 12 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s RS Aggrawal 2020 2021 Solutions. All RS Aggrawal 2020 2021 Solutions for class 6 Maths are prepared by experts and are 100% accurate.

#### Page No 172:

#### Question 1:

#### Answer:

Following are the parallel edges of the top:

$AD\parallel BC\phantom{\rule{0ex}{0ex}}ThisisbecauseADandBCwillnotintersectevenifboththeselinesegmentsareproducedindefinitelyinboththedirections.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}AB\parallel DC\phantom{\rule{0ex}{0ex}}ThisisbecauseABandDCwillnotintersectevenifboththeselinesegmentsareproducedindefinitelyinboththedirections.$

#### Page No 172:

#### Question 2:

Following are the parallel edges of the top:

$AD\parallel BC\phantom{\rule{0ex}{0ex}}ThisisbecauseADandBCwillnotintersectevenifboththeselinesegmentsareproducedindefinitelyinboththedirections.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}AB\parallel DC\phantom{\rule{0ex}{0ex}}ThisisbecauseABandDCwillnotintersectevenifboththeselinesegmentsareproducedindefinitelyinboththedirections.$

#### Answer:

$Thegroupsofparalleledgesare(AD\parallel GH\parallel BC\parallel FE),(AB\parallel DC\parallel GF\parallel HE)and(AH\parallel BE\parallel CF\parallel DG).\phantom{\rule{0ex}{0ex}}Theabovementionedgroupsofedgesareparallelbecausetheywillnotmeeteachotherifproducedinfinitelytobothsides.\phantom{\rule{0ex}{0ex}}$

#### Page No 173:

#### Question 3:

$Thegroupsofparalleledgesare(AD\parallel GH\parallel BC\parallel FE),(AB\parallel DC\parallel GF\parallel HE)and(AH\parallel BE\parallel CF\parallel DG).\phantom{\rule{0ex}{0ex}}Theabovementionedgroupsofedgesareparallelbecausetheywillnotmeeteachotherifproducedinfinitelytobothsides.\phantom{\rule{0ex}{0ex}}$

#### Answer:

(i)

$DE\parallel BC\phantom{\rule{0ex}{0ex}}Thisisbecausetheydonotintersecteachother.$

(ii)

$AB\parallel DCandAD\parallel BC\phantom{\rule{0ex}{0ex}}Thisisbecausethesepairsoflinesegmentsdonotintersecteachother.\phantom{\rule{0ex}{0ex}}$

(iii)

$AB\parallel DCandAD\parallel BC\phantom{\rule{0ex}{0ex}}Thisisbecausethesepairsoflinesegmentsdonotintersecteachother.\phantom{\rule{0ex}{0ex}}ABdoesnotintersectDCandADdoesnotintersectBC.$

(iv)

$LM\parallel RQ,RS\parallel PMandLS\parallel PQ$

These pairs of line segments are non-intersecting.

So, these pairs of lines are parallel.

(v)

$AB\parallel DC,AB\parallel EF.DC\parallel EF\phantom{\rule{0ex}{0ex}}AC\parallel BD,CE\parallel DF$

These pairs of line segments are non-intersecting.

So, these pairs of lines are parallel.

#### Page No 173:

#### Question 4:

(i)

$DE\parallel BC\phantom{\rule{0ex}{0ex}}Thisisbecausetheydonotintersecteachother.$

(ii)

$AB\parallel DCandAD\parallel BC\phantom{\rule{0ex}{0ex}}Thisisbecausethesepairsoflinesegmentsdonotintersecteachother.\phantom{\rule{0ex}{0ex}}$

(iii)

$AB\parallel DCandAD\parallel BC\phantom{\rule{0ex}{0ex}}Thisisbecausethesepairsoflinesegmentsdonotintersecteachother.\phantom{\rule{0ex}{0ex}}ABdoesnotintersectDCandADdoesnotintersectBC.$

(iv)

$LM\parallel RQ,RS\parallel PMandLS\parallel PQ$

These pairs of line segments are non-intersecting.

So, these pairs of lines are parallel.

(v)

$AB\parallel DC,AB\parallel EF.DC\parallel EF\phantom{\rule{0ex}{0ex}}AC\parallel BD,CE\parallel DF$

These pairs of line segments are non-intersecting.

So, these pairs of lines are parallel.

#### Answer:

(i) Distance between *l* and *m* is 1.3 cm.

Place the ruler so that one of its measuring edges lies along the line *l*. Hold it with one hand. Now place a set square with one arm of the right angle coinciding with the edge of the ruler. Draw the line segment PM along the edge of the set square, as shown in the figure. Then, measure the distance (PM) between *l *and *m*, which will be equal to 1.3 cm.

(ii) Distance between *l* and *m *is 1 cm.

Place the ruler so that one of its measuring edges lies along the line *l*. Hold it with one hand. Now place a set square with one arm of the right angle coinciding with the edge of the ruler. Draw the line segment PM along the edge of the set square, as shown in figure. Then, measure the distance (PQ) between *l *and *m* as 1 cm.

#### Page No 173:

#### Question 5:

(i) Distance between *l* and *m* is 1.3 cm.

Place the ruler so that one of its measuring edges lies along the line *l*. Hold it with one hand. Now place a set square with one arm of the right angle coinciding with the edge of the ruler. Draw the line segment PM along the edge of the set square, as shown in the figure. Then, measure the distance (PM) between *l *and *m*, which will be equal to 1.3 cm.

(ii) Distance between *l* and *m *is 1 cm.

Place the ruler so that one of its measuring edges lies along the line *l*. Hold it with one hand. Now place a set square with one arm of the right angle coinciding with the edge of the ruler. Draw the line segment PM along the edge of the set square, as shown in figure. Then, measure the distance (PQ) between *l *and *m* as 1 cm.

#### Answer:

At point A, AB is the perpendicular distance between *l* and *m.*

At point C, CD is the perpendicular distance between *l* and *m.*

The perpendicular distance between two parallel lines is same at all points.

∴ CD = AB = 2.3 cm

#### Page No 173:

#### Question 6:

At point A, AB is the perpendicular distance between *l* and *m.*

At point C, CD is the perpendicular distance between *l* and *m.*

The perpendicular distance between two parallel lines is same at all points.

∴ CD = AB = 2.3 cm

#### Answer:

Line segments AB and CD will intersect if they are produced endlessly towards the ends A and C, respectively.

Therefore, they are not parallel to each other.

#### Page No 173:

#### Question 7:

Line segments AB and CD will intersect if they are produced endlessly towards the ends A and C, respectively.

Therefore, they are not parallel to each other.

#### Answer:

(i) Place the ruler so that one of its measuring edges lies along the line *l*. Hold it firmly with one hand. Now place a set square with one arm of the right angle coinciding with the edge of the ruler. Draw line segments between *l *and *m* (say PM, RS, AB) with the set square.

Now, we see that PM = AB = RS.

Thus, we can say that *l* $\parallel $*m*.

(ii) In this case, we see that when we draw line segments between *l* and *m,* they are unequal, i.e. $\mathrm{PM}\ne \mathrm{RS}$.

Therefore*, l* is not parallel to *m*.

#### Page No 173:

#### Question 8:

(i) Place the ruler so that one of its measuring edges lies along the line *l*. Hold it firmly with one hand. Now place a set square with one arm of the right angle coinciding with the edge of the ruler. Draw line segments between *l *and *m* (say PM, RS, AB) with the set square.

Now, we see that PM = AB = RS.

Thus, we can say that *l* $\parallel $*m*.

(ii) In this case, we see that when we draw line segments between *l* and *m,* they are unequal, i.e. $\mathrm{PM}\ne \mathrm{RS}$.

Therefore*, l* is not parallel to *m*.

#### Answer:

(i) True

The statement is true because such lines do not intersect even when produced.

(ii) True

Perpendicular distance between two parallel lines is same at all points on the lines.

(iii) True

If the corresponding lines are produced infinitely, they will not intersect. Hence, they are parallel.

(iv) True

The corresponding lines determined by them will not intersect. Hence, they are parallel to each other.

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