Another vector proving problem:
Take any kite shape ABCD. How do I prove that the diagonals (AC and BD) are perpendicular for any kite?
I beleive it should include the dot-product of the diagonals except I dunno how to prove this for any kite.
In my opinion you can't prove a definiton:
As far as I'm informed a kite is a quadrilateral whose diagonals are perpendicular. And that's what all kites have in common.
With this definition and the calculations I gave in my previous posts you can prove that a square, a rhombus, some very special trapezoids are kites too, but you can't prove that a kite is a kite.
If you want to prove that a quadrilateral is a kite you must know some properties of the (unknown) quadrilateral. Then use the calculations to prove if the diagonals are perpendicular or not.
Hello everyone -
I have always used Plato's definition of a kite. So the vector proof you want goes like this.
Suppose that in the quadrilateral ABCD, and , and let be the mid-point of the diagonal . Then:
and
and are perpendicular.
Similarly in and are perpendicular.
is a straight line - namely, the diagonal , which is therefore perpendicular to the diagonal .
Grandad