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Geometry
Properties of Trapezoids and Kites
Trapezoid Vocabulary:
- Trapezoid: __________________________________________________________________________________
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Bases of a trapezoid: __________________________________________________________________________
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Base angles of a trapezoid: _____________________________________________________________________
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Legs of a trapezoid____________________________________________________________________________
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Isosceles trapezoid____________________________________________________________________________
1) Show that CDEF is a trapezoid.
2) Suppose the coordinates of point E are (7, 5).
What type of quadrilateral is CDEF?
If a trapezoid is isosceles, then each pair of base angles is congruent.
If trapezoid ABCD is isosceles, then A   _____ and  _____  C.
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
If A  D (or if B  C), then trapezoid ABCD is isosceles.
A trapezoid is isosceles if and only if its diagonals are_____________________.
Trapezoid ABCD is isosceles if and only if _______  ________.
3) A shelf fitting into a cupboard in the corner of kitchen is an isosceles trapezoid. Find mN, mL, and mM
MIDSEGMENT THEOREM FOR TRAPEZOIDS:
The midsegment of a trapezoid is parallel to each base and its length is half the sum of the lengths of the bases
If MN the midsegment of trapezoid ABCD, then MN || _____, MN || ______,
and MN = ____ (_______ + ______).
4) In the diagram MN , is the midsegment of trapezoid PQRS. Find MN.
-----KITE-----KITE-----KITE-----KITE-----KITE-----KITE-----KITE-----KITE-----KITE-----KITE-----KITE----Vocabulary:
- Kite:_________________________________________________________________
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End Angles:___________________________________________________________
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Side Angles:___________________________________________________________
If a quadrilateral is a kite, then its diagonals are perpendicular.
If quadrilateral ABCD is a kite, then_______  _______.
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
If quadrilateral ABCD is a kite and BC  BA , then
 A _____ C.
If a quadrilateral is a kite, then its end diagonal bisects the end angles.
If quadrilateral ABCD is a kite, then BD bisects  ________ and
5) Find mT in the kite shown below.
 ______
6) Find all angles in the picture, given:
ABC = 100  And ADC = 60 
GENERAL CONCEPTS:
Trapezoid:
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One pair of opposite sides parallel
Isosceles Trapezoid:
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Base angles congruent
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Diagonals congruent
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Can prove Isosceles Trapezoid if one pair of base angles are congruent.
Midsegment of Trapezoid connects midpoints of legs and is parallel to bases.
Formula:
Midsegment=
Kite:
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Diagonals are perpendicular
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Side angles are congruent
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End diagonal bisects end angles.
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(base 1 base 2 )
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