1. Chapter 8.5 Notes: Use Properties of Trapezoids and Kites
Goal: You will use properties of trapezoids and kites.

2. Trapezoids
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
The parallel sides are called the bases.
A trapezoid has two pairs of base angles.
The nonparallel sides are the legs of the trapezoid.

3. Ex.1: Show that ORST is a trapezoid.
If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

4. Theorem 8.14:
If a trapezoid is isosceles, then each pair of base angles are congruent.
Theorem 8.15:
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
Theorem 8.16:
A trapezoid is isosceles if and only if its diagonals are congruent.

5. Ex.2: The stone above the arch in the diagram is an isosceles trapezoid. Find

6. Ex. 3: The top of the table in the diagram is an isosceles trapezoid
Ex.3: The top of the table in the diagram is an isosceles trapezoid. Find
The midsegment of a trapezoid is the segment that connects the midpoints of its legs.

7. Theorem 8.17 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.
Midsegment = __________________________

8. Ex.4: In the diagram, is the midsegment of trapezoid PQRS. Find MN. Ex.5: In the diagram, is the midsegment of trapezoid DEFG. Find HK.

9. Ex.6: Use the diagram of trapezoid EFGH.
If EG = FH, is trapezoid EFGH isosceles? Explain.
If and , is trapezoid EFGH isosceles? Explain.

10. Kites
A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
Theorem 8.18:
If a quadrilateral is a kite, then its diagonals are perpendicular.
Theorem 8.19:
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

11. Ex. 7: Find in the kite shown below. Ex
Ex.7: Find in the kite shown below. Ex.8: In a kite, the measures of the angles are 3xo, 75o, 90o, and 120o. Find the value of x. What are the measures of the angles that are congruent.

12. Ex.9: Find in the kite shown.