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12/6/12 Unit 3 Polygons and Circles

Trapezoids

and Kites

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IsoscelesTrapezoid

Quadrilaterals

Rectangle

Parallelogram

Rhombus

Square

Flow Chart

Trapezoid

Non Parallelograms

Kite

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TrapezoidA quadrilateral with exactly one pair of parallel sides.Definition:

BaseLeg

An Isosceles trapezoid is a trapezoid with congruent legs.

Trapezoid

The parallel sides are called bases and the non-parallel sides are called legs.

Isosceles trapezoid

A Trapezoid is a quadrilateral with exactly one pair of parallel sides.

Trapezoid Terminology • The parallel sides are called BASES.   • The nonparallel sides are called LEGS.  • There are two pairs of base angles, the two touching the top base, and the two touching the bottom base.

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Properties of Isosceles Trapezoid

A B and D C

2. The diagonals of an isosceles trapezoid are congruent.

1. Both pairs of base angles of an isosceles trapezoid are congruent.

A B

CD

Base Angles

AC DB

ISOSCELES TRAPEZOID - If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

**** - Both pairs of base angles of an isosceles trapezoid are congruent. 

**** - The diagonals of an isosceles trapezoid are congruent.

**** – If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

Example 1

CDEF is an isosceles trapezoid with leg CD = 10 and mE = 95°. Find EF, mC, mD, and mF.

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The median of a trapezoid is the segment that joins the midpoints of the legs.

The median of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases.

Median

1b

2b

1 2

1( )

2median b b

Median of a Trapezoid

Example 3

102°

65°

17 in

24 in.

A B

CD

E F

Find AB, mA, and mC

Example 4

A quadrilateral is a kite if and only if it has two distinct pair of consecutive sides congruent.

• The vertices shared by the congruent sides are ends. • The line containing the ends of a kite is a symmetry line for a kite. • The symmetry line for a kite bisects the angles at the ends of the kite. • The symmetry diagonal of a kite is a perpendicular bisector of the other diagonal.

Using Properties of Kites

A

B C

D

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

mB = mC

Using Properties of Kites

D

A

B

C

Example 6

E

2

4 4

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ABCD is a Kite.

a) Find the lengths of all the sides.

b) Find the area of the Kite.

Using Properties of Kites

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Example 7

CBDE is a Kite. Find AC.

5B

C

D

EA

Using Properties of Kites

x°

125°

(x + 30)°

A

B C

D

Example 8

ABCD is a kite. Find the mA, mC, mD