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

The steps for construction are given below:

Step $1$: Draw a line

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Step $2$: Mark any point $Q$ on $AB$ and a point $P$ outside $AB$ and join $PQ$

Step $3$: Considering $Q$ as centre and any radius draw an arc to cut $AB$ at $E$ and $PQ$ at $F$.

Step $4$. Considering $P$ as centre and same radius draw an arc $IJ$ to cut $QP$ at $G$.

Step $5$. Place the pointed tip of the compass at $E$ and adjust the opening so that the pencil tip is at $F$.

Step $6$. With the same opening as in step$5$and with $G$ as centre, draw an arc cutting the arc $IJ$ at $F$.

Step $7$. Now, join $PH$ to draw a line $CD$.