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Transcript
The properties of the kite are as follows:

Two disjoint pairs of consecutive sides are congruent by definition

The diagonals are perpendicular.

The opposite angles at the endpoints of the cross diagonal are congruent (angle J and angle L).
The next two properties are called the half properties of the kite.

One diagonal (segment KM, the main diagonal) is the perpendicular bisector of the other diagonal (segment JL,
the cross diagonal). (The terms “main diagonal” and “cross diagonal” are made up for this example.)

The main diagonal bisects a pair of opposite angles (angle K and angle M).
Trapezoid


Isosceles Trapezoid
The properties of the trapezoid are as follows:

The bases are parallel by definition.

Each lower base angle is supplementary to the upper base angle on the same side.
The properties of the isosceles trapezoid are as follows:

The properties of trapezoid apply by definition (parallel bases).

The legs are congruent by definition.

The lower base angles are congruent.

The upper base angles are congruent.

Any lower base angle is supplementary to any upper base angle.

The diagonals are congruent.