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Medians and Lengths in Trapezoids

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Learn about trapezoids, isosceles trapezoids, and medians. Discover the properties of medians and how to find their lengths. Solve homework problems related to trapezoids.

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Medians and Lengths in Trapezoids

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  1. Geometry 5.5 Trapezoids

  2. Trapezoid (Defn.)Memo about medians A quadrilateral with exactly one pair of parallel sides. leg The sides are called the bases base base The other sides are called the legs leg

  3. IsoscelesTrapezoid (Defn.) A trapezoid with congruent legs.

  4. Theorem Base angles of an isosceles trapezoid are congruent.

  5. Median of a Trapezoid (Defn.) A segment that joins the midpoints of the legs. median leg leg

  6. Theorem The median of a trapezoid: 1. is parallel to the bases. 2. has a length equal to the average of the base lengths. A B XY = ½(AB + CD) median X Y C D

  7. B B A A F F E E D D C C

  8. B B A A F F E E D D C C

  9. B B A A F F E E D D C C

  10. Homework pg. 192-193 CE 1-11 WE 1-18

  11. Example Find the length of the median of the trapezoid. Median = ½(Base 1 + Base 2) 5x = 25 ½ [(x + 12) + (7x – 2)] x + 12 5x = (2) 5x = 8x + 10 5x 10x = 8x + 10 2x = 10 x = 5 7x -2

  12. A few homework problems…. Let’s do P. 192-193 #8 and #15

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