1. Trapezoids A type of Quadrilateral

2. Review of Quadrilaterals ParallelogramHas two parallel pairs of opposite sides. RectangleHas two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. SquareHas two pairs of parallel sides, four right angles, and all four sides are equal. It is also a rectangle and a parallelogram. RhombusA parallelogram with four equal sides. Not a square because it does not have four right angles.

3. Another Quadrilateral: Trapezoid Definition: A quadrilateral with exactly one pair of parallel sides, the bases. AB DC BASE LEG

4. Isosceles Trapezoid A trapezoid with congruent legs. AB DC The base angles of an isosceles trapezoid are congruent.

5. Median of a Trapezoid The segment that joins the midpoints of the legs. AB DC MN MN is the median of the trapezoid.

6. Median of a Trapezoid 1.Parallel to the bases. 2.The length is equal to the average of the bases. AB DC MN

7. Examples Given a trapezoid and its median, find the value of x. AB DC MN 16 12 x + 4 AB DC MN 18 x + 4 8

8. Examples Given a trapezoid and its median, find the value of x. AB DC MN 7x + 3 19 2x - 1 AB DC MN 3x + 2 2x + 4 2x + 1

9. Examples One angle of an isosceles trapezoid has measure of 72. Find the measures of the other angles. Two congruent angles of an isosceles trapezoid have measures 3x + 10 and 5x – 10. Find the value of x and then give the measures of all angles of the trapezoid.