### Diagonals:

The much longer diagonal the a kite is called the key diagonal and the much shorter one is referred to as the overcome diagonal. The main diagonal that a dragon is the perpendicular bisector that the cross diagonal.

You are watching: The diagonals of a kite are perpendicular bisectors of each other

That is, here the diagonal line BD¯ perpendicularly bisects the diagonal line AC¯. Example 1: In kite PQRS, QS is the main diagonal. If PR=10 units and also QO=4units what is the length PQ?

Here, QS is the perpendicular bisector that PR. Then, m∠QOP=90° and also PO=12PR=RO.

PO=12(10)

=5

ΔPOQ is a best triangle, PO=5 units, QO=4 units. Usage the Pythagorean theorem to find the size of the hypotenuse.

PQ=(PO)2+(QO)2

=52+42

=25+16

=41

The opposite angle at the ends of the cross diagonal space congruent. ### Area:

The area of a dragon is half the product that the lengths of the diagonals.

that is, if the lengths of the diagonals of a kite room d1 and also d2 respectively, then area A of the dragon is provided by the formula:

A=12d1⋅d2

Example 2:

In kite LMNO, the length of the main diagonal MO is 12 units and also that the the overcome diagonal LN is 5 units. What is the area that the dragon LMNO?

A=12(MO)(LN)

=12(12)(5)

=12(60)

=30

Therefore, the area that the kite LMNO is 30 square units.

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