Geometry 5.5 Trapezoids

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

IsoscelesTrapezoid (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

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

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

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

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

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

Homework pg CE 1-11 WE 1-18

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

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