Question

Construct an angle of ${90}^0$ at the initial point of a given ray and justify the construction.

Answer 1

Data: Constructing an angle of ${90}^0$ at the initial point of a given ray.
Steps of Construction:
1. Draw AB straight line.
2. Taking A as centre and any radius draw an arc and intersect AB at C.
3. Taking C as centre with same radius draw an arc which intersect at D.
4. With same radius taking D as centre, it intersects at E.
5. With centres E and D with same radius draw two arcs which meet both at F.
6. If AF is joined, AB straight line is the line in the point A with ${90}^0$, i.e., AF.
In the above construction $\angle DAB={60}^0$ and $\angle DAE={60}^0$.
Angular bisector of $\angle DAE$ is AF.
$\therefore \angle DAF=\angle EAF={30}^0$
$\therefore \angle BAF=\angle DAB+\angle DAE={60}^0+{30}^0$
$\therefore \angle BAF={90}^0$.