Draw a line $l .$ Draw a perpendicular to $l$ at any point on $l .$ On this perpendicular choose a point $X, 4 c m$ away from $l$ . Through $X,$ draw a line $m$ parallel to $l$ .

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Solution

Given:
A line l.
Required:
A line parallel to l which is $4$ cm away from l.
Steps of construction:
$1$ . Draw a line l.
$2$ . Take any point A on it.
$3$ . Draw a perpendicular AY to l.
$4$ . Take a point x on AY such that AX $= 4$ cm
$5$ . Draw a perpendicular to AY through X.
$6$ . $∴ m | | l$ .

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Question 2
Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

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Q. (a) Draw a line l. Draw a perpendicular on l at any point. On this perpendicular, choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

(b) Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as the centre an arc FG is drawn (as shown in the figure).

What is the relation between the length of arc DM and arc FG?
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Question 3
Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet l at S. What shape do the two sets of parallel lines enclose?

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Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X,4cm away from l. Through X, draw a line m parallel to l.

Given:A line l.Required:A line parallel to l which is 4cm away from l.Steps of construction:1. Draw a line l.2. Take any point A on it.3. Draw a perpendicular AY to l.4. Take a point x on AY such that AX=4cm5. Draw a perpendicular to AY through X.6. ∴m||l.

Draw a line $l .$ Draw a perpendicular to $l$ at any point on $l .$ On this perpendicular choose a point $X, 4 c m$ away from $l$ . Through $X,$ draw a line $m$ parallel to $l$ .