Proof of Parallelogram for Regular Quadrilateral

[SS2006]

Prove that for any regular quadrilateral, the figure formed by joining the midpoint of the four sides will always be a parallelogram

vector proof
AND
non vector proof

this is geometry and discrete mathematics btw.

 

[HallsofIvy]

Aren't YOU the one who was given that problem? What have you done on it?

 

[SS2006]

oh i can't get started
i hate proofs, i was hoping somenoe can get me started :)

 

[HallsofIvy]

What exactly do you mean by a "regular" quadrilateral?? Normal a "regular" polygon has all sides and all angles congruent. The only "regular" quadrilaterals are squares and that's much too easy. It's more interesting if you are only assuming sides are of the same length (a rhombus).

 

[ComputerGeek]

What exactly do you mean by a "regular" quadrilateral?? Normal a "regular" polygon has all sides and all angles congruent. The only "regular" quadrilaterals are squares and that's much too easy. It's more interesting if you are only assuming sides are of the same length (a rhombus).

it is even more interesting if it was any quadrilateral.

here is a hint, use mid-segements of a triangle.