Question

Construct a line parallel to the following lines from a point anywhere lying outside the lines. (a)

(b)

(c)

Answer 1

Hint: We are asked to construct a parallel line with respect to different parts in the above problem. Parallel line is the line whose all points are at a fixed distance from the given line. The parallel line need not be of the same length of the given line but all the points in that line are situated at the same fixed distance from the given line. By keeping this thing in mind, draw the parallel lines to the given lines.

Complete step-by-step answer:
In the above question, we have to construct the parallel lines with respect to the lines given above. We can draw the parallel lines anywhere outside the given line.
Now, what is a parallel line? A parallel line is always with respect to some line. It’s a relative property of a line. We always take a parallel line with respect to some other line. Now, to draw a parallel line we have to draw a line in such a way that all the points on the parallel line are equidistant from the given line.
Constructing parallel line in part (a):
The given line in the part (a) is:

Let us mark a point D lying outside the given line PQ through which we have to draw a parallel line.

Now, drawing a line through D parallel to PQ we get,

As you can see that each point on DE is at an equal and fixed distance from the line PQ.
Hence, we have drawn the line DE which is parallel to PQ through point D and this point D lies outside the line.
Constructing a parallel line in part (b),
The line given in the part (b) is:

Let us mark a point D lying outside the given line PQ through which we have to draw a parallel line.

After that, we are drawing a line from point D which is parallel to PQ as follows:

As you can see that points on the line DE are at a fixed equal distance from PQ so we DE is a parallel line.
Hence, we have constructed a parallel line DE with respect to PQ.
Constructing a parallel line in part (c),
The line given in the part (c) is:

Let us mark a point D lying outside the given line PQ through which we have to draw a parallel line.

After that, we are drawing a line from point D which is parallel to PQ as follows:

As you can see that points on the line DE are at a fixed equal distance from PQ so we DE is a parallel line.
Hence, we have constructed a parallel line DE with respect to PQ.

Note: In the above solution, we have drawn parallel lines on one side of the line PQ, you can draw on the other side of the line also. For e.g. in part (a), we have drawn parallel line as follows:

As you can see that line DE is drawn below the line PQ you can even draw the line DE above PQ in the similar way, we have drawn as above.