vector proofs

[annie]

Hi guys i was just doing some trial exams for spesh paper 1, and i came across a vector proof question on my 9th paper 

it was something like prove that OACB is a Rhombus
given that AB is perpendicular to OC

and it stumped me because i don't know the prequisite conditions in order to prove that something is a shape

can someone tell me a general list of what 'shapes' i should know and their prequisites??

eg. rhombus - must have 4 equal sides etc??

thanks alot

[Mao]

parallelogram - one pair of opposite sides are parallel and same magnitude
rectangle - parallelogram + one right angle
rhombus - four equal sides
square - rhombus + one right angle

[the triangles are pretty self explanatory]

[trinon]

Refer to image attached.

Isn't it that if you can prove that OB.AC = 0, it's a rhombus?

[ice_blockie]

Refer to image attached.

Isn't it that if you can prove that OB.AC = 0, it's a rhombus?

In short no. Draw a kite and then you will see why...