GEOMETRY: Chapter 6 6.5: Use Properties of Trapezoids and Kites

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