Construct an angle of 90° and justify the construction.
annuannu35:
put a D on the paper
you will see the sign of 90 degree on the upper part of D
draw a dot there and remove the d and join the both 0to 90
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Explanation:
Justification
Join OC and BC
Thus,
OB= BC= OC
∴ △OCB is an equilateral triangle
∴ ∠BOC= 60
o
Join OD,OC and CD
Thus,
OD= OC= DC [Radius of equal arcs]
∴ △DOC is an equilateral triangle
∴ ∠DOC= 60
o
Join PD and PC
Now,
In △ODP and △OCP
OD= OC [Radius of same arcs]
DP= CP [Arc of same radii]
OP=OP [Common]
∴ △ODP≅ △OCP [SSS congruency]
∴ ∠DOP= ∠COP [CPCT]
So, we can say that
∠DOP= ∠COP=
2
1
∠DOC
∠DOP= ∠COP=
2
1
× 60= 30
o
Now,
∠AOP= ∠BOC+ ∠COP
∠AOP= 60+ 30
∠AOP= 90
o
Hence justified.
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