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Understanding Trapezoids: Median Theorem and Properties

Discover the properties of trapezoids and the Median Theorem, which states that the median is parallel to each base and its length is the average of the base lengths. Learn how to find the median lengths in various trapezoids through examples. Understand how trapezoids with congruent legs are classified as isosceles and the properties that follow.

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Understanding Trapezoids: Median Theorem and Properties

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  1. Trapezoids

  2. Trapezoids *They have only one pair of opposite sides that are parallel base leg leg base

  3. B C E F A D The MEDIAN connects the midpoints of the legs

  4. Median Theorem for Trapezoids parallel to each base and its length is the average of the lengths of the bases

  5. EXAMPLE 1 EF is the median of trapezoid ABCD. Find EF. 22 in. A B E F C D 10 in.

  6. EXAMPLE 2 BC is the median of trapezoid MATH. Find MA. A M 15 in. B C T H 22 in.

  7. EXAMPLE 3 BC is the median of trapezoid TRAP. Find TR. T R 19 in. B C P 11 in. A

  8. If the legs are congruent then the trapezoid is ISOSCELES

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

  10. If a trapezoid is isosceles then its diagonals are congruent

  11. M A H T EXAMPLE 4 Find the missing angle measures in trapezoid MATH. 60°

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