RS Aggarwal Solutions for Class 6 Math 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 Math Parallel Lines Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RS Aggarwal Book of class 6 Math Chapter 12 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s RS Aggarwal Solutions. All RS Aggarwal Solutions for class 6 Math are prepared by experts and are 100% accurate.

#### Page No 172:

#### Question 1:

In the figure of a table given below, name the pairs of parallel edges of the top.

Figure

#### 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:

Name the groups of all possible parallel edges of the box whose figure is shown below.

Figure

#### 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:

Identify parallel line segments in each of the figures given below:

(i) Figure

(ii) Figure

(iii) Figure

(iv) Figure

(v) Figure

#### 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:

Find the distance between the parallel lines *l* and *m*, using a set square.

(i) Figure

(ii) Figure

#### 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:

In the figure, *l*||*m*. If *AB* ⊥ *l*, *CD* ⊥ *l* and *AB* = 2.3 cm, find *CD*.

Figure

#### 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:

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

Figure

#### 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:

Using a set square and a ruler, test whether *l* || *m* in each of the following cases:

(i) Figure

(ii) Figure

#### 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:

Which of the following statements are true and which are false?

(i) Two lines are parallel if they do not meet, even when produced.

(ii) Two parallel lines are everywhere the same distance apart.

(iii) If two line segments do not intersect, they are parallel.

(iv) If two rays do not intersect, they are parallel.

#### 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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