Chapter 6.5Day 1

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Chapter 6.5Day 1

• Trapezoids and Kites

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Vocabulary

• Trapezoid A quadrilateral with EXACTLY 2
  parallel sides.
• Base-angle pairs Angles in a trapezoid that are
  on the same base.

bases
legs
base angles
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Vocabulary

• Isosceles Trapezoid A trapezoid with congruent
  legs.
• Midsegment Segment that connect the midpoints
  of the legs of a trapezoid.

midsegment
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Theorems about Trapezoids

• Theorem 6.14 If a trapezoid is isosceles, then
  each pair of base angles is congruent.
• Theorem 6.15 If a trapezoid has one pair of
  congruent base angles, then it is isosceles.

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Theorems about Trapezoids

• Theorem 6.16 A trapezoid is isosceles iff. its
  diagonals are congruent.

AC ? BD
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Example 1

• Show that ABCD is a trapezoid.

• Check to see if AB ??CD and if BC ??AC. If only
  one pair of sides is parallel, then it is a
  trapezoid.

Since only one pair of sides is parallel, ABCD is
a trapezoid.
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One more Theorem

• Theorem 6.16 Midsegment Theorem for trapezoids
• The midsegment of a trapezoid is parallel to both
  bases and its length is one-half the sum of the
  lengths of the bases.

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Example 2

• Find the missing angles. ABCD is a trapezoid.
• Since ?A and ?D are adjacent and so are ?B and
  ?C, the pairs add up to 180. So

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Chapter 6.5Day 2

• Trapezoids and Kites

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Vocabulary

• Kite A quadrilateral that has 2 pairs of
  adjacent congruent sides but opposite sides are
  not congruent.

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Theorems about Kites

• Theorem 6.18 If a quadrilateral is a kite, then
  its diagonals are perpendicular.
• Theorem 6.19 If a quadrilateral is a kite, then
  EXACTLY one pair of opposite angles are congruent.

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Intro to the Pythagorean Theorem

• In a right triangle, the sum of the squares of
  the legs is equal to the square of the hypotenuse.

Example Find the missing side length.
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3
x
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Example 3

• Find the side lengths of the kite ABCD.
• Use the Pythagorean Theorem to find the
  missing sides.

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Example 3

• Find the missing angles in of the kite ABCD.
• Since all angles add up to 360 and ?A ?
  ?C, use the equation

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Summary of Quadrilaterals