Geometry 5 5 Trapezoids Trapezoid Defn Memo about

Geometry 5. 5 Trapezoids

Trapezoid (Defn. ) Memo about medians A quadrilateral with exactly one pair of parallel sides. leg The sides are called the bases The other sides are called the legs base leg

Isosceles. Trapezoid (Defn. ) A trapezoid with congruent legs.

Theorem Base angles of an isosceles trapezoid are congruent.

Median of a Trapezoid (Defn. ) A segment that joins the midpoints of the legs. leg median leg

Theorem The median of a trapezoid: 1. is parallel to the bases. 2. has a length equal to the average of the base lengths. A XY = ½(AB + CD) X C B median Y D

1. AB = 10 CD = 30 EF = x A E C 2. AB = x CD = 18 EF = 12 B F D A E C B F D

3. AB = x – 3 CD = 2 x – 4 EF = 10 4. AB = y – 4 CD = 7 y +6 A E C EF = 5 y B – 3 F E D C A B F D

5. AB = 4 x CD = 10 x EF = x 2 + 10 6. AB = x CD = 3 x EF = x 2 48 A E C B A F E D C B F D

7. One angle of an isosceles 8. Two congruent angles of trapezoid measures 68. an isosceles trapezoid Find the measures of the have measures 2 x+21 other angles. and 3 x-15. Find the value of x and then give the measures of all the angles.

Homework pg. 192 -193 CE 1 -11 WE 1 -18

Example Find the length of the median of the trapezoid. Median = ½(Base 1 + Base 2) 5 x = ½ [(x + 12) + (7 x – 2)] 5 x = 25 x + 12 (2) 5 x = 8 x + 10 10 x = 8 x + 10 5 x 2 x = 10 x=5 7 x -2

A few homework problems…. Let’s do P. 192 -193 #8 and #15