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Properties of Kites

A kite is a quadrilateral with exactly two distinct pairs of congruent consecutive sides. The angles between two congruent sides are called vertex angles and the other two angles are called nonvertex angles.

Sketch

The sketch below shows how to construct a kite. You can drag any of the red vertices to change the size or shape of the kite.

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Sketch

This sketch shows a kite that you can change by dragging vertices A, B, and D.

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Investigate

  1. Press Kite Angles to see the measurements of the four angles of the kite. What do you notice about each pair of opposite angles? Are vertex angles congruent? Are nonvertex angles congruent? Change the shape and size of the kite. Does this property still hold?
  2. Formulate the Kite Angles Conjecture: The _____ angles of a kite are _____.
  3. Press Diagonal Angle to see the diagonals of the kite and the measure of the angle between them. What do you notice about this angle? Change the shape and size of the kite. Does this property still hold?
  4. Formulate the Kite Diagonals Conjecture: The diagonals of a kite are _____.
  5. Press Diagonal Lengths to see the diagonals of the kite and the lengths of the segments on the diagonals. What do you notice about the segments? Does either diagonal bisect the other? Does this property stay the same when the shape of the kite is changed?
  6. Formulate the Kite Diagonal Bisector Conjecture: The diagonal connecting the vertex angles of kite is the _____ of the other diagonal.
  7. Press Side/Diagonal Angles to see the measures of the angles formed by the diagonals and the sides of the kite. Does either diagonal bisect any angles? Does this property stay the same when the shape of the kite is changed?
  8. Formulate the Kite Angle Bisector Conjecture: The _____ angles of a kite are _____ by a _____.