1. Trapezoids and Kites

2. Trapezoids A trapezoid is a quadrilateral with _______ _________ of ____________ ____________. Draw below labeling bases, two pairs of base angles, and legs. one pair parallel sides base leg leg base

3. Isosceles Trapezoids • When is a trapezoid isosceles? • When the two legs are congruent • What else will you know about an isosceles trapezoid? • Each pair of base angles is congruent A trapezoid is isosceles if and only if its diagonals are _____________ congruent

4. 5 4 3 2 1 1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 Example 1. Given a quadrilateral with coordinates O (0, 0), R (0, 3), S (2, 4), and T (4, 2). Draw on the coordinate plane below then prove that ORST is a trapezoid.

5. Example 2 Determine the missing angle measures for each trapezoid below.

6. Midsegment Theorem The ________________ of a trapezoid is ____________ to each base and its length is _________ the _________ of the lengths of the two bases. midsegment parallel half sum Formula: MN = 1/2(AB + CD)

7. Example 3 Determine the length of each midsegment below.

8. Example 4 Find the value of x.

9. Kites A kite is a quadrilateral that has __ _______ of consecutive ______________ sides, but _____________ sides are NOT _____________. pairs 2 congruent opposite congruent

10. Theorems If a quadrilateral is a kite, then its diagonals are _________________. perpendicular If a quadrilateral is a kite, then exactly ___ _________ of __________ angles are ___________. 1 pair opposite congruent

11. Example 5 EFGH is a kite. Find m<G. Example 6 Find the side lengths of the kite.