Question

ABCD is a square and the diagonals intersect at O. If P is a point on AB such that AO=AP, prove that 3*angle POB = angleAOP

Answer 1

Answer:

Step-by-step explanation:

First that triangle AOP is an isosceles triangle (since AO=AP)

Therefore, angle AOP=45 degree

So, angle AOP= angle APO= (180-45)/2= 67.5 degree

Now,since angle APO+ angle BPO =180 degree

We have, angle BPO=180-67.5 = 112.5 degree

Next, angle PBO= 45 degree

We have,

angle POB= 180-(angle PBO)-(angle BPO)

= 180-45-112.5=22.5 degree

So, 3* angle POB= 3*22.5 = 67.5 degree

=angle AOP

Hence Proved

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