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GEOMETRY: Chapter 6
6.5: Use Properties of
Trapezoids and Kites
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. The nonparallel
sides are the legs of the trapezoid.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 542.
Theorem 6.14
If a trapezoid is isosceles, then each pair of
base angles is congruent.
If trapezoid ABCD is isosceles,
then A  D and B  C.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
Theorem 6.15
If a trapezoid has a pair of congruent base
angles, then it is an isosceles trapezoid.
If A  D (or if B  C ),
then trapezoid ABCD is isosceles.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
Theorem 6.16
A trapezoid is isosceles if and only if its
diagonals are congruent.
Trapezoid ABCD is isosceles if and only if AC  BD.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
Ex.1: Show that XYZW is a trapezoid.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
Ex.1: Show that XYZW is a trapezoid.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
Ex. 2: The top of the table in the diagram is an
isosceles trapezoid. Find the measures of
angle N, angle O, and angle P.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
Ex. 2: The top of the table in the diagram is an
isosceles trapezoid. Find the measures of
angle N, angle O, and angle P.
Answer: 1150, 1150, 65o
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
Theorem 6.17 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.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 544.
Ex. 3:
In the diagram, segment HK is the
midsegment of trapezoid DEFG. Find HK.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 544.
Ex. 3:
In the diagram, segment HK is the
midsegment of trapezoid DEFG. Find HK.
Answer: 12 cm
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 544.
Theorem 6.18:
If a quadrilateral is a kite, then its diagonals
are perpendicular.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 545.
Theorem 6.19
If a quadrilateral is a kite, then exactly one
pair of opposite angles are congruent.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 545.
Ex. 4:
Find the measure of angle C in the kite shown.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 544.
Ex. 4:
Find the measure of angle C in the kite shown.
Answer: 68o
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 544.
6.5, p. 359