Vector proof question

[VCE_2012]

If the question asks you to prove that ABCD is a rectangle where 2 diameters (AB and CD) is within a circle with a centre O.
This is an easy proof, I essentially I proved that AC is perpendicular CB after proving that AD=CB and AC=DB. My question is do I have to prove that all the corners are perpendicular (ie proving 'AC is Perpend. to CB' 4 times-------in a sense).

To generalize my question: do we have to show that every corner within the supposed rectangle is perpendicular or would one corner be enough to show that it is a rectangle?   

[kamil9876]

Yeah right I would normally say "the same argument works for all the other corners" or something to that effect in such a situation, but I dunno if that goes down well in VCE.

To generalize my question: do we have to show that every corner within the supposed rectangle is perpendicular or would one corner be enough to show that it is a rectangle?

well because this case had symmetry (i.e each corner has essentially the same property) then you could just say "the same argument works" to deal with the others (in principle, maybe not in VCE), but obviously for different problems you may not have this, e.g: if someone asks you to verify that (0,0),(1,1),(0,2),(-1,1) is a rectangle showing one corner is right angle is not enough to prove. (indeed if i replace say (0,2) with (0,3) it's no longer a rectangle even though the angle at (0,0) is still a right angle).