Math 2 Geometry Based on Elementary Geometry, 3rd ed, by Alexander

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Math 2 GeometryBased on Elementary Geometry,
3rd ed, by Alexander Koeberlein

• 4.4
• The Trapezoid

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Definition

• A trapezoid is a quadrilateral with exactly two
  parallel sides.

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Informal Definitions

• The parallel sides of a trapezoid are bases

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Informal Definitions

• The parallel sides of a trapezoid are bases
• The non-parallel sides are legs

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Informal Definitions

• The parallel sides of a trapezoid are bases
• The non-parallel sides are legs
• Two angles that share a base as a side are called
  base angles

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Informal Definition

• When the midpoints of the two legs of a trapezoid
  are joined, the resulting segment is the median
  of the trapezoid.

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Informal Definition

• A trapezoid whose two legs are congruent, is an
  isosceles trapezoid

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Definition

• An altitude of a trapezoid is a line segment from
  one vertex of one base of the trapezoid
  perpendicular to the opposite base (or to an
  extension of that base).

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Theorem 4.4.1

• The base angles of an isosceles trapezoid are
  congruent

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Theorem 4.4.2

• The diagonals of an isosceles triangle are
  congruent.

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Theorem 4.4.3

• The length of the median of a trapezoid equals
  one-half the sum of the lengths of the two sides.

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Theorem 4.4.4

• The median of a trapezoid is parallel to each
  base.

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Theorem 4.4.5

• If two of three consecutive angles of a
  quadrilateral are supplementary, the
  quadrilateral is a trapezoid

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Theorem 4.4.6

• If two base angles of a trapezoid are congruent,
  the trapezoid is an isosceles trapezoid.

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Theorem 4.4.7

• If the diagonals of a trapezoid are congruent,
  the trapezoid is an isosceles trapezoid.
• Compare to Theorem 4.4.2

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Theorem 4.4.2

• The diagonals of an isosceles triangle are
  congruent.

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Theorem 4.4.8

• If three (or more) parallel lines intercept
  congruent segments on one transversal, then they
  intercept congruent segments on any transversal