1. Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 4.4 The Trapezoid

2. Definition A trapezoid is a quadrilateral with exactly two parallel sides.

3. Informal Definitions The parallel sides of a trapezoid are bases AB CD

4. Informal Definitions The parallel sides of a trapezoid are bases The non-parallel sides are legs AB CD

5. Informal Definitions The parallel sides of a trapezoid are bases The non-parallel sides are legs Two angles that share a base as a side are called base angles AB CD

6. Informal Definition When the midpoints of the two legs of a trapezoid are joined, the resulting segment is the median of the trapezoid.

7. Informal Definition A trapezoid whose two legs are congruent, is an isosceles trapezoid

8. Definition An altitude of a trapezoid is a line segment from one vertex of one base of the trapezoid perpendicular to the opposite base (or to an extension of that base).

9. Theorem 4.4.1 The base angles of an isosceles trapezoid are congruent

10. Theorem 4.4.2 The diagonals of an isosceles triangle are congruent.

11. Theorem 4.4.3 The length of the median of a trapezoid equals one-half the sum of the lengths of the two sides.

12. Theorem 4.4.4 The median of a trapezoid is parallel to each base.

13. Theorem 4.4.5 If two of three consecutive angles of a quadrilateral are supplementary, the quadrilateral is a trapezoid

14. Theorem 4.4.6 If two base angles of a trapezoid are congruent, the trapezoid is an isosceles trapezoid.

15. Theorem 4.4.7 If the diagonals of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. Compare to Theorem 4.4.2

16. Theorem 4.4.2 The diagonals of an isosceles triangle are congruent.

17. Theorem 4.4.8 If three (or more) parallel lines intercept congruent segments on one transversal, then they intercept congruent segments on any transversal