Question
Take any three non-collinear points $A, B, C$ and draw $\angle\text{ABC}.$ Through each vertex of the triangle, draw a line parallel to the opposite side.
✓
Answer
Steps of construction: Step I: Mark three non collinear points $A, B$ and $C$ such that none of them lie on the same line.
Step II: Join $A B, B C$ and $C A$ to form triangle $A B C$.
Step III: Parallel line to $A C$
Step IV: With $A$ as centre, draw an arc cutting $A C$ and $A B$ at $T$ and $U$, respectively.
Step V: With centre $B$ and the same radius as in the previous step, draw an arc on the opposite side of $A B$ to cut $A B$ at $X .$
Step VI: With centre $X$ and radius equal to $T U$, draw an arc cutting the arc drawn in the previous step at $Y$.
Step VII: Join $B Y$ and produce in both directions to obtain the line parallel to $A C$.
Parallel line to AB: Step I: With $B$ as centre, draw an arc cutting $B C$ and $B A$ at $W$ and $V$, respectively.
Step II: With centre $C$ and the same radius as in the previous step, draw an arc on the opposite side of $B C$ to cut $B C$ at $P .$
Step III: With centre $P$ and radius equal to $W V$, draw an arc cutting the arc drawn in the previous step at $Q .$
Step IV: Join $CQ$ and produce in both directions to obtain the line parallel to $A B$.
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