Construction 11.3 :
To construct an angle of 60° at the initial Point of a given ray.
Let us take a ray AB with initial Point A.
We want to construct a ray AC such that ∠CAB = 60°
Steps of Construction :
- Taking A as centre and some radius, draw an arc of a circle, which intersects AB at Point D.
- Taking D as Centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point E.
- Draw the ray AC Passing through E.
Thus, ∠CAB is the required angle of 60°
We need to prove ∠ CAB = 60°
Since arc AD = Arc AE
and using same radius, we drew arc DE
Thus, their radius will be the same
∴ AE = AD = DE
Therefore, ∆ EAD is an equilateral triangle
∴ ∠EAD = 60°
⇒ ∠CAB = 60°.