Properties of Trapezoids and Kites The bases of

Properties of Trapezoids and Kites The bases of a trapezoid are its 2 parallel sides A base angle of a trapezoid is 1 pair of consecutive angles whose common side is a base of the trapezoid Trapezoids have 2 pairs of base angles. The legs of a trapezoid are the 2 nonparallel sides

Figure QRST is a trapezoid • • QR and TS are bases <Q and <R are base angles <T and <S are base angles QT and RS are legs of trapezoid Q T R S

Midsegment of a trapezoid • The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs of the trapezoid

Theorem 69 -1 trapezoid midsegment theorem • The midsegment of a trapezoid is parallel to both bases and has a length that is equal to half the sum of the bases • EF is midsegment • EF is parallel to AB F • EF is parallel to D E • EF = ½(AB + DC)

Find the length of EF E F

Properties of Isosceles Trapezoids • Base angles of an isosceles trapezoid are congruent. • If trapezoid ABCD is isosceles, then <A is congruent to <B and <C is congruent to <D

Properties of Isosceles Trapezoids • The diagonals of an isosceles trapezoid are congruent

Properties of Kites • Kites are quadrilaterals with exactly 2 pairs of congruent adjacent sides • The diagonals of a kite are perpendicular

Find the lengths of the sides of the kite W 4 Z 5 5 8 Y X

practice • EF is the midsegment of trap ABCD. Find the length of CD 22 in. 38 in.

Find the measures of the angles in trapezoid 48

Find BE • AC = 17. 5, AE = 9. 6 E

Find the lengths of the sides of kite to the nearest tenth 2 7 4 2