Transcript Sect 6_5 Trapezoids and Kites - Mary Star of the Sea High School

Sect. 6.5 Trapezoids and
Kites
Goal 1
Using Properties of Trapezoids
Goal 2
Using Properties of Kites
Trapezoid definition
A Trapezoid is a quadrilateral with only
one pair of parallel sides.
Base Amgle
Base
Base Amgle
b2
Leg
Leg
h
b1
Base Amgle
Base
Base Amgle
Using Properties of Trapezoids
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.
Using Properties of Trapezoids
ISOSCELES TRAPEZOID - If the legs of a trapezoid
are congruent, then the trapezoid is an isosceles trapezoid.
Theorem - Both pairs of base angles
of an isosceles trapezoid are congruent.
Theorem – If a trapezoid has a pair of congruent base
angles, then it is an isosceles trapezoid.
Theorem - The diagonals of an isosceles
trapezoid are congruent.
Using Properties of Trapezoids
Midsegment of a Trapezoid – segment that
connects the midpoints of the legs of the
trapezoid.
A
B
Midsegment
E
F
D
C
Using Properties of Trapezoids
Theorem: Midsegment Theorem for Trapezoids
The midsegment of a trapezoid is parallel to each base and its
length is one-half the sum of the lengths of the bases.
A
B
EF || AB ; EF || DC
1
EF  ( AB  DC )
2
Midsegment
E
F
D
C
Using Properties of Kites
Using Properties of Kites
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
Theorem:
If a quadrilateral is a
kite, then exactly one
pair of opposite angles
are congruent.
mB = mC
A
C
B
D
Using Properties of Kites
Area Kite = one-half product of diagonals
1
A  d1d 2
2
D
1
Area  AC  BD
2
A
B
C
Using Properties of Kites
Example 7
C
CBDE is a Kite.
Find AC.
29
E
5
A
B
D
Using Properties of Kites
Example 8
A
ABCD is a kite. Find the
mA, mC, mD
(x + 30)°
B
C
125°
x°
D