Prove that the Diagonals of a Kite are Perpendicular

Here in this lesson we will show how to prove that the diagonals of a kite are perpendicular using the kite shown below.

Diagonals of a kite are perpendicular

A theorem we need to prove that the diagonals of a kite are perpendicular

Converse of the perpendicular bisector theorem

If a point is equidistant from the endpoints of a line segment, then the point is on the perpendicular bisector of the segment.

Given:

Kite ATBS with ASAT and BSBT

Prove:

ABST

Since ASAT, A is equidistant from the endpoints S and T.

By the converse of the perpendicular bisector theorem, A lies on the perpendicular bisector of segment ST or ST.

Since BSBT, B is equidistant from the endpoints S and T.

By the converse of the perpendicular bisector theorem, B lies on the perpendicular bisector of segment ST or ST.

Therefore, both point A and point B lie on the perpendicular bisector of segment ST or ST.

Since there is exactly one line through any two points, AB must be the perpendicular bisector of ST

We can conclude that ABST

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