Trapezoids

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TrapezoidsKites
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• Objectives
• Use properties of trapezoids
• Use properties of kites

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Special Quadrilaterals

• Parallelogram
• Rhombus
• Rectangle
• Square
• Trapezoid
• Kite

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Trapezoid

• A quadrilateral with exactly one pair of parallel
  sides

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Trapezoids

• There are two pair of base angles, two legs, and
  two bases

base
Base angle
Base angle
leg
leg
Base angle
Base angle
base
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Midsegment Theorem
The midsegment of a trapezoid is parallel to the
bases and half the sum of the bases.
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Isosceles trapezoid

• Legs are congruent

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Isosceles trapezoids

• If a trapezoid is isosceles, then each pair of
  base angles is congruent.

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Isosceles trapezoids

• 2. If a trapezoid has a pair of congruent base
  angles, then it is an isosceles trapezoid.

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Isosceles trapezoids

• 3. A trapezoid is isosceles iff its diagonals
  are congruent.

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KiteA quadrilateral that has two pairs of
consecutive congruent sides, but opposite sides
are not congruent.
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Kite

• Properties of a kite
• The diagonals of a kite are perpendicular.

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Kite
Properties of a kite 2. Exactly one pair of
opposite angles are congruent
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Kite
Properties of a kite 3. The area is one half the
product of the lengths of its diagonals
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Kite
If AC 15 DB 10 What is the area of kite ABCD?