8.5 Trapezoids and Kites

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8.5 Trapezoids and Kites
Goal 1
Using Properties of Trapezoids
Goal 2
Using Properties of Kites
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
Example 1
CDEF is an isosceles trapezoid with leg CD = 10
and mE = 95°. Find EF, mC, mD, and
mF.
Using Properties of Trapezoids
When working with a trapezoid, the height may be measured
anywhere between the two bases. Also, beware of "extra"
information. The 35 and 28 are not needed to compute this area.
1
Area of trapezoid = hb1  b2 
2
Find the area of this trapezoid.
A = ½ * 26 * (20 + 42)
A = 806
Using Properties of Trapezoids
Example 2
Find the area of a trapezoid
with bases of 10 in and 14
in, and a height of 5 in.
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 Trapezoids
Example 4
102°
A
Find AB, mA, and mC
E
17 in
B
F
65°
D
24 in.
C
Using Properties of Trapezoids
Example 5
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 6
ABCD is a Kite.
A
a) Find the lengths of all
the sides.
D
2
E 4
4
4
b) Find the area of the Kite.
C
B
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
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Area of a Rectangle: The area of a rectangle is
the product of its base and height.
A = bh
Area of a Parallelogram: The area of a
parallelogram is the product of a base and its
corresponding height.
A = bh
Area of a Triangle: The area of a triangle is one
half the product of a base and its corresponding
height.
A = ½ bh
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Area of a Trapezoid: The area of a trapezoid is
one half the product of the height and the sum of
the bases.
A = ½ h(b1 + b2)
Area of a Kite: The area of a kite is one half the
product of the length of its diagonals.
A = ½ d1 d 2
Area of a Rhombus: The area of a rhombus is
equal to one half the product of the lengths of
the diagonals.
A = ½ d1 d 2
Homework/Classwork

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