Question

Construct the angles of 90 degree at the intial point of a given ray and justify the construction. Please give image of it and i will give him brainliest

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation: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   1/2 CD, draw two arc intersecting at P.

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Join OP.

Thus, ∠AOP=90

 

Justification

Join OC and BC

Thus,

OB=BC=OC             [Radius of equal arcs]

∴△OCB is an equilateral triangle

∴∠BOC=60  

Join OD,OC and CD

Thus,

OD=OC=DC             [Radius of equal arcs]

∴△DOC is an equilateral triangle

∴∠DOC=60  

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=  1/2  ∠DOC

∠DOP=∠COP=  1/2 ×60=30  

Now,

∠AOP=∠BOC+∠COP

∠AOP=60+30

∠AOP=90  

 

Hence justified.