geometry: chapter 6 6.5: use properties of trapezoids and kites
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GEOMETRY: Chapter 6
6.5: Use Properties of Trapezoids and Kites
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 542.
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.
Theorem 6.14
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
If a trapezoid is isosceles, then each pair of base angles is congruent.
If trapezoid is isosceles,
then and .
ABCD
A D B C
Theorem 6.15
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
If (or if ),
then trapezoid is isosceles.
A D B C
ABCD
Theorem 6.16
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.
A trapezoid is isosceles if and only if its diagonals are congruent.
Trapezoid is isosceles if and only if .ABCD AC BD
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
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 544.
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.
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:
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 545.
If a quadrilateral is a kite, then its diagonals are perpendicular.
Theorem 6.19
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 545.
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
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