8_5notes_201.notebook
8­5 Use Properties of Trapezoids and Kites
March 09, 2015
isosceles trapezoid­­ congruent legs
trapezoid­­quadrilateral with exactly one pair of parallel sides
Theorem 8.14­­If a trapezoid is isosceles, then each pair of base angles is congruent
Theorem 8.15­­If a trapezoid has a pair of congruent base angles, then it is isosceles.
Theorem 8.16­­A trapezoid is isosceles iff its diagonals are congruent
Midsegment­­joins the midpoints of the legs
Theorem 8.17­­The midsegment of a trapezoid is parallel to the bases and = 1/2 the sum of the lengths of the bases
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8_5notes_201.notebook
March 09, 2015
Verify that ABCD is a trapezoid.
A(5,1)
B(­3, ­1)
C(­2, 3)
D(2, 4)
What are the endpoints of the midsegment?
A(5,1)
B(­3, ­1)
C(­2, 3)
D(2, 4)
Isosceles trapezoid ACDF
m∠1 = 3x + 5
m∠3 = 6x ­ 5
Is it isosceles?
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8_5notes_201.notebook
Kite­­a quadrilateral that has 2 pairs of consecutive congruent sides, but opposite sides are not congruent.
March 09, 2015
Theorem 8.18­­If a quadrilateral is a kite, then its diagonals are perpendicular.
Theorem 8.19­­If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
Find the lengths of the sides of the kite.
ABCD is a kite.
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8_5notes_201.notebook
March 09, 2015
HW
p546­548
5,7­15, 18­22, 25­27, 30, 32,39
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