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 problem, firstly we are drawing a line AB, then we will take any point D on AB and join it with the point C which is taken outside the line. Then by taking D as a center, we will draw an arc of convenient radius and with C as center, we will draw an arc of the same radius. Now measure the angle at D using the compass and cut the arc at C with the same measurement.

Complete step-by-step answer:
We have taken a point C which is outside the line AB and we need to draw a line through C which is parallel to AB.
So, we will be following the given steps of construction for drawing a parallel line to AB.
a)Firstly, we will be drawing a line segment AB of any measurement and take a point C outside line AB.

b)Now, we will be taking any point D on line AB and then we will join point C to point D.

c)In the next step, we will be drawing an arc with point D as the center and convenient radius which cuts line AB at point E and line CD at point F.

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

e)Now, we will measure the arc EF and draw the equal arc at point C which cuts at point J.

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

Therefore, the line ‘l’ is the line asked in the question which is parallel to AB.

Note: The method of drawing parallel lines by using corresponding angles should be known clearly in order to get the construction right in this question. We need to be very careful while measuring the arc of EF and cutting the same arc of length at point C. Also, the most important point to remember is that the radius should be the same as the arc at D and the arc at point C.
This problem can be solved alternatively by drawing a perpendicular line to line AB through point C and obtaining the perpendicular line as DC. After this, we will be drawing a perpendicular line as DC and we will get a line which will be parallel to line AB and passing through point C.