1 2-12-15 polygons and quadrilaterals unit trapezoids and kites
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IsoscelesTrapezoid
Quadrilaterals
Rectangle
Parallelogram
Rhombus
Square
Flow Chart
Trapezoid
Non Parallelograms
Kite
A Trapezoid is a quadrilateral with exactly one pair of parallel sides.Trapezoid Terminology • The parallel sides are called BASES. • The nonparallel sides are called LEGS. • There are two pairs of base angles, the two touching the top base, and the two touching the bottom base.
ISOSCELES TRAPEZOID - If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.
**** - Both pairs of base angles of an isosceles trapezoid are congruent.
**** - The diagonals of an isosceles trapezoid are congruent.
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The median of a trapezoid is the segment that joins the midpoints of the legs.
The median of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases.
Median
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2b1 2
1( )
2median b b
Median of a Trapezoid
A quadrilateral is a kite if and only if it has two distinct pair of consecutive sides congruent.
• The vertices shared by the congruent sides are ends. • The line containing the ends of a kite is a symmetry line for a kite. • The symmetry line for a kite bisects the angles at the ends of the kite. • The symmetry diagonal of a kite is a perpendicular bisector of the other diagonal.
Using Properties of Kites
D
A
B
C
Example 3
E
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ABCD is a Kite.
a) Find the lengths of all the sides.
b) Find the area of the Kite.