6-6 Vocabulary Kite Trapezoid Base of a trapezoid Leg of a trapezoid Base angle of a trapezoid Isosceles trapezoid Midsegment of a trapezoid

6-6 Properties of Kites & Trapezoids Geometry

Kite Kites- a quad with 2 pairs of consecutive @ sides, but opp sides are not @. __ __ __ __ __

Properties of Kites Thm 6-6-1 If a quad is a kite then its diagonals are . T __ __ _ _ __ __

Prop. Of Kites Thm 6-6-2 X W ) ( Y If a quad is a kite then exactly one pair of opp ‘s are @. X W ) ( Y Always the angles between two non  sides Z

Ex. 1 Lucy is framing a kite with wooden dowels. She uses two dowels that measure 18 cm, one dowel that measures 30 cm = JM, & 2 dowels that measure 27 cm. To complete the kite, she needs a dowel to place along KL. She has a dowel that is 36 cm long. About how much wood will she have left over after cutting the last dowel? K K 18cm J M M L 3.6 cm 27cm

Ex. 2 In kite ABCD, Find each measure. a.) B b.) C c.) A D a)76 degrees b)115 degrees c)63 degrees

Trapezoids __ leg base < < base leg __ Trapezoid- a quadrilateral with exactly one pair of ll sides. Bases- ll sides Legs- non ll sides Isosceles trapezoid- a trapezoid with @ legs Base s – come in pairs. base < < base leg __

Thm 6-6-3 If a trapezoid is an isosceles trapezoid, then it’s base angles (each pair) are  . W X > __ __ Z > Y W @ X and Z @ Y

Thm 6-6-4 If a trapezoid has a pair of @ base angles, then it’s an isosceles trapezoid. > ) ( >

Thm 6-6-5 A trapezoid is isosceles iff its diagonals are @. A B If Seg AC @ seg DB, then ABCD is isosceles and if ABCD is isosceles, then seg AC  seg DB. D C

Midsegments A B Seg MN is the midseg of ABCD N M C D Midsegement of a trapezoid- segment that connects the midpts of the legs. A B Seg MN is the midseg of ABCD N M C D

Ex. 3 A.) Find B 100° C D A B.) KB=21.9 & MF = 32.7. Find FB. F J K M 80 degrees 10.8

Ex. 4 A.) Find the value of a so that PQRS is isosceles. ∠P = (a²+27)° , ∠S=(2a²-54)° Q P S R B.) AD = 12x – 11, & BC = 9x – 2. Find the value of x so that ABCD is isosceles. A B C D a=+-9 b) x= 3

Thm 6-6-6 Trapezoid Midsegment Thm The midseg of a trapezoid is ll to the bases and its length is ½ the sum of the base lengths. B A __ > __ M __ N > __ D > C MN || AB || DC and MN = ½ (AB+DC)

Ex. 5 Find EF 13.5 A D E F B 8 C 10.75

Assignment