1. 6.5: Use Properties of Trapezoids and Kites
GEOMETRY: Chapter 6
6.5: Use Properties of Trapezoids and Kites

2. 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, P. 542.

3. Theorem 6.14
If a trapezoid is isosceles, then each pair of base angles is congruent.
Image taken from: Geometry. McDougal Littell: Boston, P. 543.

4. 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, P. 543.

5. 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, P. 543.

6. Ex.1: Show that XYZW is a trapezoid.
Image taken from: Geometry. McDougal Littell: Boston, P. 543.

7. Ex.1: Show that XYZW is a trapezoid.
Image taken from: Geometry. McDougal Littell: Boston, P. 543.

8. 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, P. 543.

9. 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, P. 543.

10. 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, P. 544.

11. Ex. 3:
In the diagram, segment HK is the midsegment of trapezoid DEFG. Find HK.
Image taken from: Geometry. McDougal Littell: Boston, P. 544.

12. 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, P. 544.

13. 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, P. 545.

14. 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, P. 545.

15. 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, P. 544.

16. 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, P. 544.

17. 6.5, p. 359