RS Aggarwal Solutions: Parallel Lines | Mathematics (Maths) Class 6 PDF Download

 Page 1


Points to Remember :
Parallel Lines. Two lines in  a plane which do not meet even when produced in definitely in either
direction, are known as parallel lines. The perpendicular distance between two parallel lines is the
same everywhere.
Parallel Segments. Two segments are parallel, if the corresponding lines determined by them are
parallel.
Parallel Rays. Two rays are parallel, if the corresponding lines determined by them are parallel.
EXERCISE 12
| | DG ; AD | | GH | | BC | | EF
Q. 3. Identify the parallel lines segments in
each of the figure given below :
Sol. (i) In the given figure,
DE | | BC
Q. 1. In the adjoining figure of a table, given
below, name pairs of parallel edges of
the top.
Sol. In the given figure, the pairs of parallel
edges are :
AB | | CD and BC | | AD
Q. 2. Name the groups of all possible parallel
edges of the box, whose figure is shown
below.
Sol. In the given figure, pairs of all possible
parallel edges are :
AB | | HE | | DC | | GF ; BE | | CF | | AH
Page 2


Points to Remember :
Parallel Lines. Two lines in  a plane which do not meet even when produced in definitely in either
direction, are known as parallel lines. The perpendicular distance between two parallel lines is the
same everywhere.
Parallel Segments. Two segments are parallel, if the corresponding lines determined by them are
parallel.
Parallel Rays. Two rays are parallel, if the corresponding lines determined by them are parallel.
EXERCISE 12
| | DG ; AD | | GH | | BC | | EF
Q. 3. Identify the parallel lines segments in
each of the figure given below :
Sol. (i) In the given figure,
DE | | BC
Q. 1. In the adjoining figure of a table, given
below, name pairs of parallel edges of
the top.
Sol. In the given figure, the pairs of parallel
edges are :
AB | | CD and BC | | AD
Q. 2. Name the groups of all possible parallel
edges of the box, whose figure is shown
below.
Sol. In the given figure, pairs of all possible
parallel edges are :
AB | | HE | | DC | | GF ; BE | | CF | | AH
(ii) In the given figure,
AB | | DC ; AD | | BC
(iii) In the given figure,
AB | | DC ; AD | | BC
(iv) In the given figure,
LM | | RQ, MP | | RS, PQ | | SL.
(v) In the given figure,
AB | | CD, CD | | EF, AC | | BD, CE | | DF,
AB | | EF.
Q. 4. Find the distance between the parallel
lines l and m, using a set square.
Sol. (i) Place the rular 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
rular. Read off the distance between l
and m on the set square which is 1.7cm.
(ii) Place the rular so that one of the
measuring edges of the rular lies along
the line l. Hold it firmly with one hand
and place a set square with one arm of
the right angle coinciding with the edge
of the rular. Read off the distance
between the lines l and m on the set
square which is 1.2 cm.
Q. 5. In figure, l | | m. If AB  l, CD  l and
AB = 2.3 cm., find CD.
Sol. It is given that l | |  m.
Also AB  l i.e. AB is the perpendicular
distance between two parallel lines l and
m.
Page 3


Points to Remember :
Parallel Lines. Two lines in  a plane which do not meet even when produced in definitely in either
direction, are known as parallel lines. The perpendicular distance between two parallel lines is the
same everywhere.
Parallel Segments. Two segments are parallel, if the corresponding lines determined by them are
parallel.
Parallel Rays. Two rays are parallel, if the corresponding lines determined by them are parallel.
EXERCISE 12
| | DG ; AD | | GH | | BC | | EF
Q. 3. Identify the parallel lines segments in
each of the figure given below :
Sol. (i) In the given figure,
DE | | BC
Q. 1. In the adjoining figure of a table, given
below, name pairs of parallel edges of
the top.
Sol. In the given figure, the pairs of parallel
edges are :
AB | | CD and BC | | AD
Q. 2. Name the groups of all possible parallel
edges of the box, whose figure is shown
below.
Sol. In the given figure, pairs of all possible
parallel edges are :
AB | | HE | | DC | | GF ; BE | | CF | | AH
(ii) In the given figure,
AB | | DC ; AD | | BC
(iii) In the given figure,
AB | | DC ; AD | | BC
(iv) In the given figure,
LM | | RQ, MP | | RS, PQ | | SL.
(v) In the given figure,
AB | | CD, CD | | EF, AC | | BD, CE | | DF,
AB | | EF.
Q. 4. Find the distance between the parallel
lines l and m, using a set square.
Sol. (i) Place the rular 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
rular. Read off the distance between l
and m on the set square which is 1.7cm.
(ii) Place the rular so that one of the
measuring edges of the rular lies along
the line l. Hold it firmly with one hand
and place a set square with one arm of
the right angle coinciding with the edge
of the rular. Read off the distance
between the lines l and m on the set
square which is 1.2 cm.
Q. 5. In figure, l | | m. If AB  l, CD  l and
AB = 2.3 cm., find CD.
Sol. It is given that l | |  m.
Also AB  l i.e. AB is the perpendicular
distance between two parallel lines l and
m.
Again CD  l i.e. CD is the perpendicular
distance between two parallel lines l and
m.
But the perpendicular distance between
two parallel lines is always same
everywhere.
 CD = AB = 2.3 cm.
Q. 6. In the Fig. do the segments AB and CD
intersect ? Are they parallel ? Give
reasons for your answer.
Sol. In the given figure, we see that the line
segments AB and CD do not intersect.
But, the corresponding lines determined
by them will clearly intersect. So, the
segment AB and CD are not parallel.
Q. 7. Using set square and a rular, test whether
l | | m in each of the following cases.
Sol. (i) Place the rular so that one of its
measuring edges lies along of its
measuring edges lies along the line l.
Hold it firmly and place a set square with
one arm of the right angle coinciding
with the edge of the rular. Draw the line
segment AB along the edge of the set
square as shown in figure.
Slide the set square along the rular and
draw some more segments CD and EF.
We observe that AB = CD = EF.
 l | | m.
(ii) Place the rular so that one of its
measuring edges lies along the line l.
Hold it firmly and place a set square with
one arm of the right angle conciding with
the edge of the rular. Draw the line
segment AB along the edge of the set
square.
Slide the set square along the rular and
draw some more segments CD and EF
as shown in the figure.
We observe that AB  CD  EF
Hence l is not parallel to m.
Q. 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 same
distance apart.
(iii) If two segments do not intersect, they
are parallel.
(iv) If two rays do not intersect, they are
parallel.
Page 4


Points to Remember :
Parallel Lines. Two lines in  a plane which do not meet even when produced in definitely in either
direction, are known as parallel lines. The perpendicular distance between two parallel lines is the
same everywhere.
Parallel Segments. Two segments are parallel, if the corresponding lines determined by them are
parallel.
Parallel Rays. Two rays are parallel, if the corresponding lines determined by them are parallel.
EXERCISE 12
| | DG ; AD | | GH | | BC | | EF
Q. 3. Identify the parallel lines segments in
each of the figure given below :
Sol. (i) In the given figure,
DE | | BC
Q. 1. In the adjoining figure of a table, given
below, name pairs of parallel edges of
the top.
Sol. In the given figure, the pairs of parallel
edges are :
AB | | CD and BC | | AD
Q. 2. Name the groups of all possible parallel
edges of the box, whose figure is shown
below.
Sol. In the given figure, pairs of all possible
parallel edges are :
AB | | HE | | DC | | GF ; BE | | CF | | AH
(ii) In the given figure,
AB | | DC ; AD | | BC
(iii) In the given figure,
AB | | DC ; AD | | BC
(iv) In the given figure,
LM | | RQ, MP | | RS, PQ | | SL.
(v) In the given figure,
AB | | CD, CD | | EF, AC | | BD, CE | | DF,
AB | | EF.
Q. 4. Find the distance between the parallel
lines l and m, using a set square.
Sol. (i) Place the rular 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
rular. Read off the distance between l
and m on the set square which is 1.7cm.
(ii) Place the rular so that one of the
measuring edges of the rular lies along
the line l. Hold it firmly with one hand
and place a set square with one arm of
the right angle coinciding with the edge
of the rular. Read off the distance
between the lines l and m on the set
square which is 1.2 cm.
Q. 5. In figure, l | | m. If AB  l, CD  l and
AB = 2.3 cm., find CD.
Sol. It is given that l | |  m.
Also AB  l i.e. AB is the perpendicular
distance between two parallel lines l and
m.
Again CD  l i.e. CD is the perpendicular
distance between two parallel lines l and
m.
But the perpendicular distance between
two parallel lines is always same
everywhere.
 CD = AB = 2.3 cm.
Q. 6. In the Fig. do the segments AB and CD
intersect ? Are they parallel ? Give
reasons for your answer.
Sol. In the given figure, we see that the line
segments AB and CD do not intersect.
But, the corresponding lines determined
by them will clearly intersect. So, the
segment AB and CD are not parallel.
Q. 7. Using set square and a rular, test whether
l | | m in each of the following cases.
Sol. (i) Place the rular so that one of its
measuring edges lies along of its
measuring edges lies along the line l.
Hold it firmly and place a set square with
one arm of the right angle coinciding
with the edge of the rular. Draw the line
segment AB along the edge of the set
square as shown in figure.
Slide the set square along the rular and
draw some more segments CD and EF.
We observe that AB = CD = EF.
 l | | m.
(ii) Place the rular so that one of its
measuring edges lies along the line l.
Hold it firmly and place a set square with
one arm of the right angle conciding with
the edge of the rular. Draw the line
segment AB along the edge of the set
square.
Slide the set square along the rular and
draw some more segments CD and EF
as shown in the figure.
We observe that AB  CD  EF
Hence l is not parallel to m.
Q. 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 same
distance apart.
(iii) If two segments do not intersect, they
are parallel.
(iv) If two rays do not intersect, they are
parallel.
Sol. (i) True (ii) True (iii) False (iv) False.
You Must Know
Transversal. A line which intersects two or more given lines in a plane at different points is
called a transversal to the given lines.
Angles made by a transversal to Two Lines :
Let l and m be two lines and a transversal t intersecting them at the points L and M respectively.
Mark the angles 1 to 8 as shown in the figure.
(i) Interior Angles. The angles whose arms include line segment LM are called interior angles.
So 3, 4, 5, 6 are interior angles.
(ii) Exterior Angles. The angles whose arms do not include the line segment LM are called
exterior angles. So, 1, 2, 7 and 8 are exterior angles.
(iii) Corresponding Angles. The pairs ( 1 and 5), ( 2 and 6), ( 4 and 8) and ( 3 and
7) are the possible pairs of corresponding angles.
(iv) Alternate Interior Angles. The pairs ( 3 and 5), and ( 4 and 6) are the possible pairs
of alternate interior angles.
(v) Alternate Exterior Angles. The pairs ( 2 and 8) and 1 and 7 are the pairs of alternate
exterior angles.
Some Results : (a) If a transversal cuts two parallel lines then :
(i) Alternate angles are equal.
(ii) Corresponding angles are equal.
(iii) The sum of the interior angles on the same side of the transversal is equal to 180º.
(b) If a transversal cuts two lines such that any one of the following conditions is satisfied :
(i) Pairs of alternate angles are equal ;
(ii) Pairs of corresponding angles are equal ;
(iii) The sum of the interior angles on the same side of the transversal is 180º, then the two lines
are parallel.