Construct an angle of 90 degree at the initial point of a given ray and justify the construction

Construct an angle of 90 degree at the initial point of a given ray an

1.	Construct an angle of 90 degree at the initial point of a given ray and justify the construction
Answer» Given: A ray OA.Required: To construct an angle of 90° at O and justify the construction.Steps of Construction:1.\xa0Taking O as centre and some radius, draw an arc of a circle, which intersects OA, say at a point B.2.\xa0Taking B as centre and with the same radius as before, draw an are intersecting the previously drawn are, say at a point C.3.\xa0Taking C as centre and with the same radius as before, draw an arc intersecting the arc drawn in step 1, say at D.4.\xa0Draw the ray OE passing through C. Then ∠EOA = 60°.5.\xa0Draw the ray OF passing through D. Then ∠FOE = 60°.6. Next, taking C and D as centres and with the radius more than\xa0\xa0ID, draw arcs to intersect each other, say at G.7. Draw the ray OG. This ray OG is the bisector of the angle ∠FOE, i.e., ∠FOG\xa0Justification:(i) Join BC.Then. OC = OB = BC (By construction)∴ ∆COB is an equilateral triangle.∴ ∠COB = 60°.∴ ∠EOA = 60°.(ii) Join CD.Then, OD = OC = CD (By construction)∴ ∆DOC is an equilateral triangle.