2.13: Kite Properties
Learning Objectives
- Identify and classify a kite.
- Identify the relationship between diagonals in kites.
- Identify the relationship between opposite angles in kites.
Kites
Among all of the quadrilaterals you have studied so far, kites are probably the most unusual.
Kites have no parallel sides, but they do have congruent sides. Kites are defined by two pairs of congruent sides that are adjacent to each other, instead of opposite each other.
Kites have two pairs of congruent sides that are ________________________ to each other.
A vertex angle is between two congruent sides and a non-vertex angle is between sides of different lengths:
The vertex angle of a kite is between the two __________________________ sides.
The non-vertex angle of a kite is between the sides of _______________________ lengths.
Kites have a few special properties that can be proven and analyzed just as the other quadrilaterals you have studied. This lesson explores those properties.
Diagonals in Kites
The relationship of diagonals in kites is important to understand. The diagonals are not congruent, but they are always perpendicular. In other words, the diagonals of a kite will always intersect at right angles.
Theorem for Kite Diagonals
The diagonals of a kite are perpendicular.
The diagonals of a kite are _____________________________________.
The diagonals of a kite intersect each other at ____________ angles.
Opposite Angles in Kites
In addition to the bisecting property, one other property of kites is that the non-vertex angles are congruent.
So, in the kite \begin{align*}PART\end{align*} above, \begin{align*}\angle PAR \cong \angle PTR\end{align*}.
The non-vertex angles in a kite are _______________________________.
Reading Check:
On the diagram below, mark the following...
- Two pairs of congruent sides
- One pair of congruent angles
- Right angles
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