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Exploring Isosceles Trapezoids & Midsegments in Geometry

Discover the properties of isosceles trapezoids with parallel bases and congruent legs. Learn about midsegments connecting midpoints of legs and how to calculate their lengths. Solve for x to make a trapezoid isosceles and find angle measures. Practice examples included.

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Exploring Isosceles Trapezoids & Midsegments in Geometry

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  1. Geometry 6-6 Trapezoids • Only one pair of parallel sides (called bases) • Non-parallel sides are called legs • Base angles share a common base

  2. Isosceles Trapezoid • Legs are congruent • Each pair of base angles are congruent • Top and bottom angles are supplementary • Diagonals are congruent B A AC ≅BD D C

  3. Examples AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles. Find mA.

  4. Midsegment of a Trapezoid • A midsegment of a trapezoid connects the midpoints of the two legs (also called a median). Base Midsegment Midpoint Midpoint Base

  5. Length of a Midsegment • The midsegment of a trapezoid is the average of the two bases. Base 1 Midsegment Base 2

  6. Example Find the length of EF. 10 F E 24

  7. Example Find the length of AB. B A 19.5 32

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