base leg > > AB C D <D AND <C ARE ONE PAIR OF BASE ANGLES. When the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

 If a trapezoid is isosceles, then each pair of base angles is congruent. A B CD

SR P Q 50° > > m<R = 50 0 m<P = m<Q = 130 0

 A trapezoid is isosceles if and only if its diagonals are congruent. A B CD

 The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the base. A B C D M N

 The midsegment of the trapezoid is RT. Find the value of x. 7 R T x 14 x = ½ (7 + 14) x = ½ (21) x = 21 / 2

 The midsegment of the trapezoid is ST. Find the value of x. 8 S T 11 x 11 = ½ (8 + x) 22 = 8 + x 14 = x

 A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are NOT congruent.

 If a quadrilateral is a kite, then its diagonals are perpendicular  If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

 GHJK is a Kite. Find m<G and m<J. G H J K 132° 60° Since m<G = m<J, 2(m<G) + 132° + 60° = 360° 2(m<G) + 192° = 360° 2(m<G) = 168° m<G = 84°

 GHJK is a Kite Find the side length. G H J K 12 10