9.4 Properties of Kites and Trapezoids, Study notes of Analytical Geometry

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9.4 Properties of Kites and Trapezoids

What makes a kite a kite?

Theorem

If a quadrilateral is a kite, then its diagonals

are perpendicular.

N

Lucy is framing a kite

with wooden dowels. She

uses two dowels that

measure 18 cm, one

dowel that measures 30

cm, and two dowels that

measure 27 cm. To

complete the kite, she

needs a dowel to place

along KL. She has a

dowel that is 36 cm long.

About how much wood

will she have left after

cutting the last dowel?

In kite ABCD , m ∠

DAB = 54 °,

and m∠ CDF = 52°.

Find m ∠

BCD.

m∠ BCD = 76 °

Find m ∠

ABC.

m∠ ABC = 115 °

Find m ∠

FDA.

m∠ FDA = 63°

If the legs of a trapezoid are congruent, the

trapezoid is an isosceles trapezoid. The

following theorems state the properties of an

isosceles trapezoid.

Theorem

If a quadrilateral is an isosceles trapezoid, then each

pair of base angles are congruent.

Theorem

A trapezoid is isosceles if and only if its diagonals are

congruent.

Find m ∠

A.

FB = 10.

Find m ∠

F.

m∠ F = 131 °

Find the value of a so

that PQRS is isosceles.

HW # 97

p. 473 # 1-

Ch 9 Test -- coming soon!