Question
Construct an angle of $90^\circ $ and bisect it.
✓
Answer
Construction steps:
$1.$ Draw a line $O A$.
$2.$ Take a point $B$ on $O A$. With $B$ as the centre and any convenient radius, draw an arc cutting $O A$ at $M$ and $N$.
$3.$ With N as the centre and radius more than half of $MN$ , draw an arc.
$4.$ With $M$ as the centre and the same radius as before, draw another arc to cut the previous arc at $W.$
$5.$ Draw $WB$, meeting the arc at $S$. Produce it to $C.$
$\angle ABC$ is the required angle of $90^{\circ} \angle ABC$ is the required angle of $90^{\circ}$.
$6.$ With $S$ as the centre and radius more than half of $S N$, draw an arc.
$7.$ With $N$ as centre and the same radius as in step $(6)$, draw another arc, cutting the previously drawn arc at point $X .$
$8.$ Draw $B X$ and produce it to point $D$. Ray $B D$ is the angle bisctor of $\angle A B C$. Ray $B D$ is the angle bisctor of $\angle A B C$. Ray $B D$ is the angl bisctor of $\angle ABC$. Ray $BD$ is the angle bisctor of $\angle ABC$.
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