Question

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

Answer 1

Answer:

Please mark as brilliant i have attached pic

Answer 2

Answer:

Construction →

To construct an angle 90° , following the given steps :

• Draw a ray OA .
• Take O as a centre with radius , draw an arc DCB is that cuts OA at B .
• with B as s centre with same radius , mark a point C on the are DCB .
• with C as centre with the same radius , mark a point D on the are DCB .
• take C and D as centre , draw two arcs which intersect each other with same radius at P .
• finally , the ray OP is joined which an angle 90° with OP is formed .

Justification →

To prove angle POA = 90°

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 angle BOC = 60°

Similarly ,

OD = DC = OC

Therefore , DOC is an equilateral triangle

So , that angle DOC = 60°

from SSS triangle congruence rule

triangle OBC = OCD

So , angle BOC = angle DOC ( by C.P.C.T )

Therefore , angle COP = 1/2 angle DOC = 1/2 ( 60° )

angle COP = 30°

To find the angle POA = 90°

angle POA = angle BOC + angle COP

angle POA = 60° + 30°

angle POA = 90°

hence , justified .