Properties of Kites

Definition: A kite is a quadrilateral with two pairs of congruent, consecutive sides.

Kites also have the following properties:
– Perpendicular diagonals
– Exactly one pair of congruent opposite angles.
– The longer diagonal bisects the shorter diagonal
– The longer diagonal bisects the vertex anglesKite_on_its_Side.gif

Example: Find the measure of ∠D and the length of side AB given the figure is a kite.

images-q=tbn-ANd9GcQ5d2rq1i7mEOMBLAmlxlK_AmvaSKSCyrexsDYnZZvC3MtTrL_g.png

Solution:

Use the information provided in the figure and the properties of kites to find the measure of ∠D and the length of side AB.

Step 1: We know kites are quadrilaterals, so the sum of interior angles will equal 360 degrees. We also know kites have one pair of congruent, opposite angles. Using this information we can write the following equation, using “x” for the unknown congruent angles (∠D and ∠B):
55 + 105 + x + x = 360
160 + 2x = 360
2x = 200
∠D = 100

Step 2: We also know that kites have two pairs of congruent, consecutive sides. To find the length of side AB, we can refer to side AD.
As side AD has a length of 7cm, we can determine that side AB also has a length of 7 cm.
Side AB = 7 cm

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