Properties

The last of the special quadrilaterals to examine is the kite.   A kite has two pair of unique congruent adjacent sides.  See the figure below. 

 KiteDef

A parallelogram also has two pair of congruent sides, but its congruent sides are opposite each other.  Therefore, a kite is not a parallelogram.  A rhombus has two pair of congruent sides, but the pairs are congruent to each other.  A kite's congruent pairs have different lengths.

There are three theorems that are special to a kite.

  • A kite has one pair of opposite angles congruent.

KiteAngCong

  • The diagonals of a kite are perpendicular.

KiteDiagPerp

  • The longest diagonal of a kite bisects the other. KiteDiagBisect

 This theorem can be proved true by drawing in a diagonal and using congruent triangles.  Take a moment to verify why this statement is true.

This theorem can be proved true by using the idea that K is the same distance from E and I and the definition of a perpendicular bisector.  Take a moment to verify why this statement is true. This theorem can be proved true by using the same concepts that were used for the perpendicular diagonals.  Take a moment to verify why this statement is true.

 

 

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