Draw any line segment PQ . Without measuring PQ , construct a cop… - Vidyadip

Question

Draw any line segment $\overline{\mathrm{PQ}}$. Without measuring $\overline{\mathrm{PQ}}$, construct a copy of $\overline{\mathrm{PQ}}$.

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Answer

$i.\ $Given $\overline{\mathrm{PQ}}$ whose length is not known.
$ii.\ $Fix the compasses pointer on $P$ and the pencil end on $Q$. The opening of the instrument now gives the length of $\overline{\mathrm{PQ}}$.
$iii.\ $Draw any line $l$. Choose a point $A$ on $l$. Without changing the compasses setting, place the pointer on $A$.
$iv.\ $Strike an arc that cuts $l$ at a point, say, $B$. Now $\overline{A B}$ is a copy of $\overline{\mathrm{PQ}}$.

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