1. Construct an angle of 90° at the initial
point of a given ray and justify the
construction.
Answers
STEPS−OF−CONSTRICTION:
Draw a ray OA
Take O as a centre with any radius, draw an arc DCB is that cuts OA at B.
With B as a centre with the same radius, mark a point C on the arc DCB.
With C as a centre and the same radius, mark a point D on the arc DCB.
Take C and D as centre, draw two arcs which intersect each other with the same radius at P.
Finally, the ray OP is joined which makes an angle 90° with OP is formed
\huge\star{\purple{\underline{\mathfrak{Justification:}}}}⋆
Justification:
In order to prove this draw a dotted line from the point O to C and O to D and the angles formed are:
From the construction, it is observed that
OB= BC = OC
Therefore OBC is an equilateral triangle
So that, ∠BOC = 60°.
Similarly,
OD= DC = OC
Therefore DOC is an equilateral triangle
So that, ∠DOC = 60°.
From SSS triangle congruence rule
△OBC ≅ OCD
∠BOC= ∠DOC
Therefore, ∠COP = ½ ∠DOC = ½ (60°).
∠COP = 30°
To find the ∠POA = 90°:
∠POA =∠BOC+ ∠COP
∠POA = 60° +30°
∠POA =90°
\large\star{\red{\mathrm{Hence, justified!}}}⋆Hence,justified!
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