Question

Take any three non – collinear points P, Q, and R. Through each point draw a line parallel to the line joining the other two points.

Answer 1

Hint: Join the three points using a pencil and a scale to make a triangle. Through each point of the triangle, use the trick to draw a line parallel to the given line passing through a point. Repeat the process for all the endpoints of the triangle.

Complete step-by-step answer:

We have three collinear points P, Q, and R. We have to draw a line passing through a point, parallel to the line joining the other two points for all the points.
We will join all three points using a pencil and a scale to form a triangle.

We will now extend all the three line segments PR, QR, and PQ to PA, BR, and PC respectively.

We will firstly draw a line passing through point R parallel to line PQ.
Taking P as centre and radius smaller than the length of PR, we will draw an arc cutting PR at point E and PQ at point D.

Taking R as the centre and same radius as the previous arc, we draw another arc cutting the extended line AR at G.

We will adjust the compass width as DE and with the same radius, taking G as the centre, we cut the arc at point F.

We will join the point R and F using a pencil and a scale and extend it a bit. Thus, the line RJ passes through R and is parallel to line PQ.

We will now repeat the procedure as above to draw a line passing through P, parallel to QR, and passing through Q parallel to PQ.

Hence, we have lines PK, QL, and RJ passing through points P, Q, and R and parallel to the line joining the other two points, as shown in the figure above.

Note: One must keep in mind that all the lines should be straight and must be drawn with a pencil and scale. It’s necessary to label all the vertices during each step of construction. All the constructions must be clear and non – messy and should be drawn using a pencil only.