Draw any line segment \( \overline{\mathrm{AB}} \). Mark any point \( \mathrm{M} \) on it. Through \( \mathrm{M} \), draw a perpendicular to \( \overline{\mathrm{AB}} \). (use ruler and compasses)
To do:
We have to draw a perpendicular to $\overline{AB}$.
Solution:
Steps of construction:
(i) Let us draw a line segment $\overline{AB}$ and mark a point M on it.
(ii) Now, by taking M as a centre let's draw an arc intersecting the line segment $\overline{AB}$ and name the intersecting points as C and D respectively.
(iii) Now, by pointing the pointer of the compasses at C as the centre with a measure of radius greater than C to M let's draw an arc.
(iv) Similarly, by pointing the pointer at D as the centre with the same measure let's draw another arc. let these two arcs intersect each other at point E.
(v) Then, join the points M and E.
(vi) Therefore, $\overline{EM}$ is perpendicular to $\overline{AB}$.
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