Question

Draw a line, say AB take a point c outside it. Through C, draw a line parallel to AB using ruler and compasses only.

Answer 1

Hint:For the above question, first we will draw a line AB, then we will take a point D on AB and join it with the point C which is outside. Then with D as center, draw an arc of convenient radius and with C as center, draw an arc of the same radius. Now measure the angle at D using the compass and cut the arc at C with that measurement.

Complete step-by-step answer:
We have been given a point C which is outside the line AB and we will have to draw a line through C and parallel to AB.
Now we will follow the given steps of construction.
(a) We will draw a line segment AB and take a point C outside AB.

(b) We will take any point D on AB and join C to D.

(c) We will draw an arc with D as the center and convenient radius which cuts AB at E and CD at F.

(d) Once again, we will draw an arc with C as the center and the same radius while drawing an arc at D. It cuts the CD at I.

(e) We will measure the arc EF and draw the equal arc at point C which cuts at J.

(f) We will join JC to draw a line saying ‘l’.

Therefore, the line ‘l’ is the required line which is parallel to AB.

Note: The method of drawing parallel lines using corresponding angles must be known properly in order to get the construction right in this question. Be careful while measuring the arc of EF and cutting the same arc of length at point C. Also, remember that the radius should be the same as the arc at D and the arc at point C. We can also solve this by drawing a perpendicular line to line AB through point C. Then we will obtain the perpendicular line as DC. Then again, drawing a perpendicular line as DC, we will get a line which will be parallel to AB and passing through C.