6.5: Use Properties of Trapezoids and Kites

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Presentation transcript:

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

A trapezoid is a quadrilateral with exactly one pair of parallel sides 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. 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. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 543.

A trapezoid is isosceles if and only if its diagonals are congruent. Theorem 6.16 A trapezoid is isosceles if and only if its diagonals are congruent. 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 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 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.

If a quadrilateral is a kite, then its diagonals are perpendicular. 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.

Find the measure of angle C in the kite shown. Ex. 4: Find the measure of angle C in the kite shown. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 544.

Find the measure of angle C in the kite shown. 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