Download Honors Geometry Section 4.5 (3) Trapezoids and Kites

Honors Geometry Section 4.5 (3)
Trapezoids and Kites
Two special types of quadrilaterals
that are NOT parallelograms are
trapezoids and kites.
A trapezoid is a quadrilateral with
exactly one pair of opposite sides
parallel.
bases
The sides that are parallel are called _______.
The nonparallel sides are called ______.
legs
The angles at each end of a base are
base angles
called _____________.
A midsegment of a trapezoid is the
segment joining the midpoints of
the two legs.
Theorem
The midsegment of a trapezoid is parallel
to the bases and the length of the
midsegment is equal to ½ the sum of the
bases.
AB // ED // FC
FC  1

AB  ED 
2
2 FC  AB  ED
An isosceles trapezoid is a
trapezoid that has congruent legs.
Theorem
In an isosceles trapezoid, the base
angles that share a common base are
congruent.
Note: For any trapezoid the angles
that share a common leg are
_____________.
supplementary
Theorem
The diagonals of an isosceles
trapezoid are congruent.
Example 1: Find the value of x, y and z in
this isosceles trapezoid.
y  43
z  137
2(40 x  19)  4 x  16  8 x  31
80 x  38  12 x  47
68 x  85
x  85  1.25
68
A kite is a quadrilateral with two
pairs of congruent adjacent sides
and noncongruent opposite sides.
Theorem
The diagonals of a kite
are perpendicular.
Example 2: Find the perimeter of the kite.
18  13.5  c
2
2
2
c  22.5
13.5  32.4  c
2
2
2
c  35.1
P  2(22.5)  2(35.1)  115.2