Post on 22-Dec-2015
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.
The sides that are parallel are called _______.
The nonparallel sides are called ______.
The angles at each end of a base are called _____________.
bases
legs
base angles
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.
FCEDAB ////
EDABFC
EDABFC
221
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.
43y
137z
25.16885
8568
47123880
318164)1940(2
x
x
xx
xxx
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.
222 5.1318 c5.22c
222 4.325.13 c1.35c
2.115)1.35(2)5.22(2 P