Download Properties of Kites Theorems

6-6 Properties of Kites and Trapezoids
Kite—a quadrilateral with exactly two pairs of congruent consecutive sides.
Properties of Kites Theorems
1. If a quadrilateral is a kite, then its diagonals are perpendicular.
In a kite, one diagonal is the perpendicular bisector of the other diagonal.
Segment AC is the perpendicular
bisector of BD
2. If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
Trapezoid—a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is
called a base. The non-parallel sides are the legs.
Base angles of a trapezoid—two consecutive angles whose common side is a base.
http://www.mrlarkins.com/geometry/InteractiveTextbook/Ch06/06-05/PH_Geom_ch06-05_Obj1.html
Isosceles trapezoid—A trapezoid with congruent legs.
http://www.google.com/imgres?q=base+angles+of+a+trapezoid&hl=en&biw=1366&bih=622&
Isosceles Trapezoids Theorems
1. If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent.
http://www.google.com/imgres?q=base+angles+of+a+trapezoid&hl=en&biw=1366&bih=622&tbm=isch&tbnid=QOSXsg7oeD2ggM:&imgrefurl=
2. If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles.
< A is congruent to < B, therefore
ABDC is an isosceles trapezoid.
3. A trapezoid is isosceles if and only if its diagonals are congruent.
Segment BC is congruent to
segment AD, therefore trapezoid
ABDC is an isosceles trapezoid.
Trapezoid Midsegment theorem—The midsegment of a trapezoid is parallel to each base and
its length is one half the sum of the lengths of the bases.
http://www.google.com/imgres?q=trapezoid+midsegment+theorem&num=10&hl=en&biw=1366
http://www.google.com/imgres?q=trapezoid+midsegment+theorem&num=10&hl=en&biw=