Download Geometry Lesson 6.6.notebook

Geometry Lesson 6.6.notebook
February 18, 2015
Trapezoids and Kites
Trapezoid ­ a quadrilateral with exactly one pair of parallel sides.
The parallel sides are called the bases.
The non­parallel sides are called the legs.
The base angles are the pair of angles formed by one of the parallel sides and the two legs.
are one pair of base angles In trapezoid ABCD, and
from the other pair of base angles. and and
The two angles Isosceles Trapezoid ­ A trapezoid where the legs are congruent.
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Geometry Lesson 6.6.notebook
February 18, 2015
Isosceles Trapezoid Theorems
A. If a trapezoid is isosceles, then each pair of base angles are congruent.
B. If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid.
C. A trapezoid is isosceles if and only if its diagonals are congruent.
ABCD is an isosceles trapezoid if AC = BD and AD=BC.
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Geometry Lesson 6.6.notebook
February 18, 2015
FGHJ is an isosceles trapezoid.
Find:
a.
b. KH
Quadrilateral ABCD has vertices A(­3,4), B(2,5), C(3,3), and D(­1,0). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid.
1. Show only one pair of sides are parallel.
Only one pair of parallel sides, so it is a trapezoid. Now, to determine if it is isosceles either show the legs are congruent or the diagonals are congruent.
Since the diagonals are not congruent, ABCD is not isosceles.
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Geometry Lesson 6.6.notebook
February 18, 2015
Midsegment of a Trapezoid ­ the segment that connects the midpoints of the legs of a trapezoid.
is the midsegment of trapezoid ABCD.
Trapezoid Midsegment Theorem ­ The midsegment of a trapezoid is parallel to each base and its measure is one­half the sum of the lengths of the bases.
Suppose EF = 15 and CD = 18.2, find AB.
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Geometry Lesson 6.6.notebook
February 18, 2015
Kite ­ a quadrilateral with exactly two pairs of congruent consecutive sides.
Properties of Kites
Theorem 1 ­ If a quadrilateral is a kite, then its diagonals are perpendicular.
Theorem 2 ­ If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent. The pair of congruent opposite angles is always the two angles between the non­congruent sides.
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Geometry Lesson 6.6.notebook
February 18, 2015
Find Find XY.
a. Find
, if b. If BT = 5 and TC = 8, find CD.
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Geometry Lesson 6.6.notebook
February 18, 2015
P. 440 8­21, 35­50
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