1. TRAPEZOIDS Recognize and apply the properties of trapezoids. Solve problems involving the medians of trapezoids. Trapezoid building blocks Text p. 439 JOHN B. CORLEY

2. A trapezoid is a quadrilateral with exactly one pair of parallel sides. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY

3. The base angles are formed by the base and one of the legs. The non-parallel sides are called legs. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY AB CD base leg  A and  B are base angles  C and  D are base angles

4. If the legs are congruent, a trapezoid is an isosceles trapezoid. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY AB C D

5. If the legs are congruent, a trapezoid is an isosceles trapezoid. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY Both pairs of base angles of an isosceles trapezoid are congruent AB C D

6. If the legs are congruent, a trapezoid is an isosceles trapezoid. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY The diagonals of an isosceles trapezoid are congruent AB C D

7. Example 1 Identify Trapezoids JKLM is a quadrilateral with vertices J(-18, -1), K(-6, 8), L(18, 1), and M(-18, -26). 10 8 6 4 2 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -25-20-15-10-5510152025 J K L M a.Verify that JKLM is a trapezoid b.Determine whether JKLM is an isosceles trapezoid (-18, -1) (-6, 8) (18, 1) (-18, -26)

8. MEDIANS OF TRAPEZOIDS median The segment that joins the midpoints of the legs of a trapezoid is called the median. The median of a trapezoid can also be called a midsegment. AB C D

9. MEDIANS OF TRAPEZOIDS AB C D THEOREM The median of a trapezoid is parallel to the bases and its measure is one half the sum of the measures of the bases. E F Example: EF = ½(AB + DC)

10. Example 2 Median of a Trapezoid Q R S T X Y QRST is an isosceles trapezoid with median XY 12 34 a.Find TS if QR = 22 and XY = 15

11. Example 2 Median of a Trapezoid Q R S T X Y QRST is an isosceles trapezoid with median XY 12 34 b.Find m  1, m  2, m  3, and m  4 if m  1 = 4a – 10 and m  3 = 3a + 32.5

12. Kites A B C D A Kite is a quadrilateral with exactly two distinct pairs of adjacent congruent sides. In kite ABCD, diagonal BD separates the kite into two congruent triangles. Diagonal AC separates the kite into two non-congruent isosceles triangles.