Transcript Trapezoids and Kites

Trapezoids
Chapter 6.6
Trapezoid
Def:
A Quadrilateral with exactly one pair of parallel sides.
 The parallel sides are called the bases.
 The non-parallel sides are called the legs.
 A trapezoid has two pairs of base angles.
If the legs are congruent, then it is called an
isosceles trapezoid.
Trapezoid
Base
Base Angles
Base Angles
Base
Isosceles Trapezoid
Isosceles Trapezoid Theorem
Isosceles Trapezoid  Each pair of base angles are .
Another Isosceles Trapezoid
Theorem
Isosceles Trapezoid  Its diagonals are .
Midsegment Theorem for Trapezoids
The Median or Midsegment of a trapezoid is //
to each base and is one half the sum of the
lengths of the bases. (average of the bases)
1
Midsegment = (b1  b2 ) or (b1  b2 )
2
2
B1
Midsegment
B2
DEFG is an isosceles trapezoid with
median (midsegment) MN
Find m1, m2, m3, and m4
if m1 = 3x + 5 and m3 = 6x – 5.
WXYZ is an isosceles trapezoid with
median (midsegment)
Find XY if JK = 18 and WZ = 25.
ABCD is a quadrilateral with vertices A(5, 1),
B(–3, 1), C(–2, 3), and D(2, 4). Determine
whether ABCD is an isosceles trapezoid.
Explain.
Identify Trapezoids
slope of
slope of
slope of
Answer: Exactly one pair of opposite sides are parallel,
So, ABCD is a trapezoid.
Identify Trapezoids
Use the Distance Formula to
show that the legs are
congruent.
Answer: Since the legs are
not congruent,
ABCD is not an
isosceles trapezoid.
A. QRST is a quadrilateral with
vertices Q(–3, –2), R(–2, 2), S(1, 4), and
T(6, 4). Verify that QRST is a trapezoid.
A. yes
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C. cannot be determined
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B. QRST is a quadrilateral with
vertices Q(–3, –2), R(–2, 2), S(1, 4), and
T(6, 4). Determine whether QRST is an
isosceles trapezoid.
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Median of a Trapezoid
A. DEFG is an isosceles trapezoid
with median (midsegment)
Find DG if EF = 20 and MN = 30.
B. DEFG is an isosceles trapezoid. Find
m1, m2, m3, and m4 if m1 = 3x + 5
and m3 = 6x – 5.
Consecutive Int. Angles Thm.
Substitution
Combine like terms.
Divide each side by 9
Answer: If x = 20, then m1 = 65 and m3 = 115.
Because 1  2 and 3  4, m2 = 65
and m4 = 115.
A. WXYZ is an isosceles trapezoid with
median (midsegment)
Find XY if JK = 18 and WZ = 25.
A. XY = 32
B. XY = 25
C. XY = 21.5
D. XY = 11
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B. WXYZ is an isosceles trapezoid.
If m2 = 43, find m3.
A. m3 = 60
B. m3 = 34
C. m3 = 43
D. m3 = 137
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Homework
Chapter 6.6
Pg 359
3,4, 17-22