A kite is a specific type of quadrilateral that has two pairs of adjacent sides that are equal in length. Here are the properties of a kite, such as FGHJ:
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Two Pairs of Congruent Sides: A kite has two pairs of consecutive (adjacent) sides that are equal in length. For kite FGHJ, this means that FG = FJ and GH = HJ.
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Diagonals: The diagonals of a kite have special properties:
- One diagonal (the one connecting the vertices where the unequal sides meet) bisects the other diagonal.
- The diagonal connecting the vertices of the congruent sides is usually the longer diagonal, and it bisects the other diagonal at a right angle.
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Angle Properties: Kites have the following angle properties:
- The angles between the pairs of equal sides are congruent. For instance, in kite FGHJ, angles FGJ and FHJ are equal, and angles GHF and JHF are equal.
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Symmetry: A kite has one line of symmetry, which is along the axis formed by the longer diagonal. This line of symmetry divides the kite into two mirror-image halves.
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Area: The area of a kite can be calculated using the lengths of the diagonals: \[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \] where \(d_1\) and \(d_2\) are the lengths of the diagonals.
These properties distinguish kites from other quadrilaterals, such as trapezoids, which have only one pair of opposite sides that are parallel and do not necessarily have pairs of congruent consecutive sides.
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