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# Draw a right angle and construct its bisector.

To do:

We have to draw a right angle and construct its bisectors.

Solution:

__Steps of construction:__

(i) Let us draw a line of any length $l$ and mark a point $O$ on it.

(ii) By taking compasses with any measure of radius let us draw an arc from point $O$ and mark the point of intersection of this arc with line $l$ as point $P$.

(iii) By taking compasses with the same radius as before let us draw another arc from point $P$ and let us mark the point of intersection of the previous arc with this arc as point $R$.

(iv) Now, by taking compasses with the same radius as before let us draw another arc from point $R$ and mark the point of intersection of this arc with the first arc as $S$.

(v) Now, by taking the compasses of the same radius as before from the points $R$ and $S$ let us draw an arc and mark the point of intersection of this arc with the previous arc as point $T$.

(vi) Now, let us join point $S$ and point $T$. Therefore, $\overline{ST}$ forms a right angle with the line $l$.

(vii) Let $\overline{ST}$ intersect the first arc at point $U$. Now, by taking compasses with a radius greater than half of the length from point $U$ to point $R$ let us draw an arc from point $U$ and point $R$ this intersects each other at a point $V$.

(viii) Now, let us join points $P$ and $W$. Therefore, the required bisector of formed right angle $\overline{TU}$ is formed.

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