Question

Draw a line segment $PQ=6.5$ cm. Take any point $M$ outside it. Using ruler and compasses, draw a line through $M$ parallel to $PQ$.

Answer 1

Steps of construction :

(1) Draw a line segment $PQ$ of length $6.5cm$ using the ruler and take a point $M$ outside $PQ$

(2)Take any point $N$ on $PQ$ and join $M$ to $N$

(3)with $N$ as center and take convenient radius, draw a arc cutting $PQ$ at $X$ and $MN$ at $Y$

(4)with $M$ as center and same radius as in step-3 draw a arc AB cutting $MN$ at $Z$

(5)with the same arc $XY$, draw the equal arc cutting $AB$ at $W$

(6)Join $MW$ to draw a line $l$

thus the required parallel line $l$ to line segment $PQ$ is drawn