8-5: Trapezoids

Essential Quote: It’s a trap!

8-5: Trapezoids TRAPEZOID: A quadrilateral with exactly one

pair of parallel sides. BASES: The pair of parallel sides in a trapezoid LEGS: The nonparallel sides of a trapezoid BASE ANGLES: Pairs of angles that lie on the

same base.base

base

legleg

base angles

base angles

8-5: Trapezoids MEDIAN: The segment that joins the midpoints

of the legs. The median of a trapezoid it equal to one half the

sum of the two bases

Example: Find MN if DE = 12 and FG = 18 ½(12 + 18) ½(30) MN = 15

D

M

G

E

N

F

MN = ½(DE + GF)

8-5: Trapezoids In some case, you will be asked to find the

length of a leg given the median and the other leg

Example: Find FG if MN is a median, MN = 22 and DE = 14 22 = ½(14 + FG) 44 = 14 + FG FG = 30

D

M

G

E

N

F

MN = ½(DE + GF)

8-5: Trapezoids ISOSCELES TRAPEZOID: A trapezoid where the two

legs are congruent. In this case, each pair of base angles are congruent. Example: Find the missing angles in trapezoid TRAP

P and A are base angles Since this is an isosceles trapezoid,

the base angles are equal P = 60 T and R are also equal A trapezoid is a quadrilateral,

meaning its angles add up to 360˚. x + x + 60 + 60 = 360 2x + 120 = 360 (combine like terms) 2x = 240 (subtract 120 each side) x = 120 (divide by 2) T = 120 and R = 120

8-5: Trapezoids Assignment

Worksheet 8-5