sect. 6.5 trapezoids and kites goal 1 using properties of trapezoids goal 2 using properties of...
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Sect. 6.5 Trapezoids and Kites
Goal 1 Using Properties of Trapezoids
Goal 2 Using Properties of Kites
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Trapezoid definition
A Trapezoid is a quadrilateral with only one pair of parallel sides.
Base
Base
LegLeg
1b
2b
h
AmgleBase
AmgleBase
AmgleBase
AmgleBase
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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.
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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 - The diagonals of an isosceles trapezoid are congruent.
Theorem – If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
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Using Properties of Trapezoids
Midsegment
A B
CD
E F
Midsegment of a Trapezoid – segment that connects the midpoints of the legs of the trapezoid.
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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.
Midsegment
A B
CD
E F
)(2
1
||;||
DCABEF
DCEFABEF
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Using Properties of Kites
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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 symmetry diagonal of a kite is a perpendicular bisector of the other diagonal.
•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.
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Using Properties of Kites
A
B C
D
Theorem:
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
mB = mC
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Using Properties of Kites
D
A
B
C
Area Kite = one-half product of diagonals
212
1ddA
BDACArea 2
1
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Using Properties of Kites
29
Example 7
CBDE is a Kite. Find AC.
5B
C
D
EA
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Using Properties of Kites
x°
125°
(x + 30)°
A
B C
D
Example 8
ABCD is a kite. Find the mA, mC, mD