Proving a Quadrilateral Is a Kite

Now that we have seen some symmetries and properties of kites, we can use them to check if a quadrilateral is a kite. Let's go through each of these one at a time $-$ after all, there aren't that many!

First, verify that the diagonals are perpendicular. If you are given the coordinate of the vertices, this becomes trivial with slopes.

Next, find the side lengths of the quadrilateral, or at least prove that for some naming $ABCD$, we have $AB=BC$ and $CD = DA$; i.e. there are two adjacent pairs of equal sides.

These two properties are both simple to check with coordinates. Without coordinates one can simply use synthetic properties such as the Pythagorean theorem and similar triangles.