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Understanding Trapezoids: Properties and Characteristics

Explore the properties of trapezoids, defined as quadrilaterals with one pair of parallel sides. Learn how the bases are the parallel sides, while the non-parallel sides are referred to as legs. Discover the characteristics of isosceles trapezoids, where legs are congruent and both pairs of base angles are equal. The diagonals of isosceles trapezoids are also congruent. Additionally, understand trapezoid medians that connect the midpoints of the legs, remaining parallel to the bases, and being half the sum of the base lengths.

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Understanding Trapezoids: Properties and Characteristics

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  1. 8-6 Trapezoids

  2. Properties of Trapezoids • Quadrilateral with one pair of parallel sides • The bases are the parallel sides • The non parallel sides are legs • If the legs are congruent then the trapezoid is isosceles • Both pairs of base angles of an isosceles trapezoid are congruent • The diagonals of an isosceles trapezoid are congruent

  3. Isosceles Trapezoid A B D C

  4. Medians • The segment that joins the midpoints of the legs of a trapezoid • The median of a trapezoid is parallel to the bases • The measure of the median is one-half the sum of the measures of the bases A B E F D C

  5. Example: • DEFG is an isosceles trapezoid with median MN • Find DG if EF=20 and MN=30 • Find m<1, m<2, m<3 and m<4 if m<1=3x+5 and m<3=6x-5 E F 3 4 M N 1 2 D G

  6. G F Proof C D • CDFG is an isosceles trapezoid with bases CD and FG. Prove that

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