Geometry B Bellwork
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Transcript of Geometry B Bellwork
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Geometry B Bellwork
1) State whether the quadrilateral is a parallelogram. Explain your reasoning.
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6.5 Trapezoids and Kites
Geometry
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Using properties of trapezoids
A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases. A trapezoid has two pairs of base angles. For instance in trapezoid ABCD D and C are one pair of base angles. The other pair is A and B. The nonparallel sides are the legs of the trapezoid.
base
base
legleg
A B
D C
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Trapezoid Theorems
Theorem 6-15 The base angles of
an isosceles trapezoid are congruent.
A ≅ B, C ≅ D
A B
D C
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Trapezoid Theorems
Theorem 6-16 The diagonals of an
isosceles trapezoid are congruent.
ABCD is isosceles, AC BD.≅
A B
D C
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Geometry B Bellwork
2) State the definition of a trapezoid. Label its parts.
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Kite theorems
Theorem 6-17 The diagonals of a
kite are perpendicular
AC BD
B
C
A
D
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EX. Given an isosceles trapezoid.Find the measure of each angle…
1)
77° 1
23
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OYO… Given an isosceles trapezoid find the measures of the missing angles
2)
1 49 °
2 3
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EX. Given a kite, find the measures of the numbered angles
45°
2
1 3
65º
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OYO…Given a kite, find the measures of the numbered angles
52°
21 3
65º
4
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Solve for x.
3)
4)
60° (3x + 15)°
(x + 6)°
2x°
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Ex. 2: Using properties of trapezoids
Show that ABCD is a trapezoid. Compare the slopes of opposite sides.
The slope of AB = 5 – 0 = 5 = - 1 0 – 5 -5
The slope of CD = 4 – 7 = -3 = - 1 7 – 4 3
The slopes of AB and CD are equal, so AB ║ CD.
The slope of BC = 7 – 5 = 2 = 1 4 – 0 4 2
The slope of AD = 4 – 0 = 4 = 2 7 – 5 2
The slopes of BC and AD are not equal, so BC is not parallel to AD.
So, because AB ║ CD and BC is not parallel to AD, ABCD is a trapezoid.
8
6
4
2
5 10 15A(5, 0)
D(7, 4)
C(4, 7)
B(0, 5)
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Midsegment of a trapezoid
The midsegment of a trapezoid is the segment that connects the midpoints of its legs.
midsegment
B C
DA
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Theorem 6.17: Midsegment of a trapezoid
The midsegment of a trapezoid is parallel to each base and its length is one half the sums of the lengths of the bases.
MN║AD, MN║BC MN = ½ (AD + BC)
NM
A D
CB
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EX. Midsegment of a trapezoid
Find the midsegment
AD= 28, BC=12 MN = ½ (AD + BC) NM
A D
CB
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Ex. 3: Finding Midsegment lengths of trapezoids
LAYER CAKE A baker is making a cake like the one at the right. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer be?
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Ex. 3: Finding Midsegment lengths of trapezoids
Use the midsegment theorem for trapezoids.
DG = ½(EF + CH)=½ (8 + 20) = 14” C
D
E
D
G
F
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Ex. 5: Angles of a kite
Find mG and mJ
in the diagram at the
right.
SOLUTION:
GHJK is a kite, so G ≅ J and mG = mJ.2(mG) + 132° + 60° = 360°Sum of measures of int. s of a quad. is
360°
2(mG) = 168°Simplify
mG = 84° Divide each side by 2.
So, mJ = mG = 84°
J
G
H K132° 60°
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Reminder:
Quiz after this section