Warm Up Find the distance between the points (-2, -5) and (4, 3).

6.5 Trapezoids & Kites

Trapezoid: quadrilateral with exactly one pair of parallel sides Bases: parallel sides Legs: non-parallel sides

Trapezoid: quadrilateral with exactly one pair of parallel sides Bases Angles: 2 angles that share the same base Adjacent angles (one from each base) are supplementary. 115⁰ 65⁰

Isosceles Trapezoid: trapezoid where the legs are congruent *If the legs are congruent then the base angles are congruent

Properties of an Isosceles Trapezoid One pair of opposite sides are parallel Diagonals are congruent

Ex.1 CDEF is an isosceles trapezoid where CD and FE are the legs. If CD = 10 and m ∠ E = 95°, then find EF, m ∠ C, m ∠ D, and m ∠ F. F E D C

Ex.2 The vertices of trapezoid WXYZ are W(-1, 2), X(3, 0), Y(4, -3), and Z(-4, 1). Show that WXYZ is an isosceles trapezoid.

Midsegment of a Trapezoid: a segment that connects the midpoints of the legs The midsegment is parallel to the bases. ** The midsegment is the average of the two parallel bases**

Ex.3 A potter crafts a trapezoidal relish dish, placing a divider, shown by AB, in the middle of the dish. How long must the divider be to ensure that it divides the legs in half? 8in 10in A B

Warm Up Find the missing side in the triangle below. 5 m x 13 m

Kite: a quadrilateral where the diagonals are perpendicular Properties: *Exactly one pair of opposite angles are congruent *Diagonal bisects the non-congruent angles

Kite: a quadrilateral where the diagonals are perpendicular Properties: *2 pair of consecutive sides congruent *The diagonal connecting the congruent angles is bisected by the other diagonal

Ex. 1 GHJK is a kite. Find HP.

Ex. 2 Find the length of each side of the kite. If m ∠ ADC = 92° and m ∠ ABC = 128°, find m ∠ BAD and m ∠ BCD.

Ex. 3 RSTU is a kite. Find m ∠ R, m ∠ S, m ∠ T.

Ex. 4* DEFG is a kite. Find the value of x and y.

You may use a “Property Cheat Sheet” on tomorrow’s quiz. Only 1 sheet of paper allowed.

Warm Up The vertices of KLMN are K(-3, 5), L(0, 7), M(2, 7), and N(3, 5). Is KLMN a trapezoid? If it is, tell whether it is isosceles and find its midsegment length.