Trapezoids and Kites

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Trapezoids and Kites

• 1/16/13
• Mrs. B

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Objectives

• Use properties of trapezoids.
• Use properties of kites.

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Using properties of trapezoids

• A trapezoid is a quadrilateral with exactly one
  pair of parallel sides called bases.
• A trapezoid has two pairs of base angles. Ex. ?D
  and ?C
• And ?A and ?B.
• The nonparallel sides are the legs of the
  trapezoid.

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Using properties of trapezoids

• If the legs of a trapezoid are congruent, then
  the trapezoid is an isosceles trapezoid.

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Isosceles Trapezoid

• If a trapezoid is isosceles, then each pair of
  base angles is congruent.
• ?A ? ?B, ?C ? ?D

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Isosceles Trapezoid

• If a trapezoid is isosceles, then adjacent angles
  (not bases) are supplementary.
• ltA ltD 180
• ltB ltC 80

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Ex. 1 Using properties of Isosceles Trapezoids

• Given, angle X is 50
• Find ltR, lt P and ltQ,

50
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Isosceles Trapezoid

• A trapezoid is isosceles if and only if its
  diagonals are congruent.
• ABCD is isosceles if and only if AC ? BD.

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Midsegment of a trapezoid

• The midsegment of a trapezoid is the segment that
  connects the midpoints of its legs.

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Theorem 6.17 Midsegment of a trapezoid

• The midsegment of a trapezoid is parallel to each
  base and its length is one half the sums of the
  lengths of the bases.
• MNAD, MNBC
• MN ½ (AD BC)

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Ex. 3 Finding Midsegment lengths of trapezoids

• LAYER CAKE A baker is making a cake like the one
  at the right. The top layer has a diameter of 8
  inches and the bottom layer has a diameter of 20
  inches. How big should the middle layer be?

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(No Transcript)
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Ex. 3 Finding Midsegment lengths of trapezoids
E

• Use the midsegment theorem for trapezoids.
• DG ½(EF CH)
• ½ (8 20) 14

F
D
G
D
C
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Using properties of kites

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

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Kite theorems

• Theorem 6.18
• If a quadrilateral is a kite, then its diagonals
  are perpendicular.
• AC ? BD

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Kite theorems

• Theorem 6.19
• If a quadrilateral is a kite, then exactly one
  pair of opposite angles is congruent.
• ?A ? ?C
• ?B not ?D

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Ex. 4 Using the diagonals of a kite

• WXYZ is a kite so the diagonals are
  perpendicular. You can use the Pythagorean
  Theorem to find the side lengths.
• WX
• XY

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Ex. 5 Angles of a kite

• Find m?G and m?J
• in the diagram.

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