Vaishali Bhatia and Rupesh Pathak Solutions for Chapter: Constructions, Exercise 2: Exercise 12.1

Draw a line $p$ parallel to a line $q$ and passing through the point $P$ ($P$ should not lie on line $q$).

Draw a perpendicular to line $l$. Take a point $A$ on this perpendicular such that $A$ is $3 \mathrm{cm}$ away from$l$. Through $A$ draw a line $m$ parallel to $l$.

Construct $l$ parallel to $m$ such that the distance between $l \text{and} m$ is $4.5 \mathrm{cm}$ by using set squares and rules.

Construct $l$ parallel to $m$ such that the distance between $l \text{and} m$ is $4.5 \mathrm{cm}$ by using compasses and ruler.

Draw $PQ=5 \mathrm{cm}$. At $P$ draw $SP\perp PQ$ such that $SP=4 \mathrm{cm}$. Through $S$ draw $SR\parallel PQ$ and cut off $SR=5 \mathrm{cm}$. Join $RQ$. Is it $4 \mathrm{cm}$? What is this figure $PQRS$ called?

Take a point $A$ not lying on a line $l$. Through $A$, draw a line m parallel to line $l$, now join $A$ with any point $B$ on $l$ and consider a point $C$ on line $m$. Through $C$ draw a line n parallel to $AB$ and name it as $CD$ which is line $n$. Can you name the figure enclosed between $l, n, m \text{and} AB$?