construct an angle of 90° at the initial point of a given ray and justify the construction
Answers
ANSWER
Steps of construction
Draw a line segment OA.
Taking O as center and any radius, draw an arc cutting OA at B.
Now, taking B as center and with the same radius as before, draw an arc intersecting the previously drawn arc at point C.
With C as center and the same radius, draw an arc cutting the arc at D.
With C and D as center and radius more than
2
1
CD, draw two arc intersecting at P.
Join OP.
Thus, ∠AOP=90
o
Justification
Join OC and BC
Thus,
OB=BC=OC [Radius of equal arcs]
∴△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.
thank you (*_*)
