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Understanding Trapezoids: Properties, Medians, and Isosceles Forms

In this lesson, we explore the fascinating world of trapezoids, a unique quadrilateral with exactly one pair of parallel sides. Learn to identify and apply the properties of trapezoids, including the characteristics of bases, legs, and base angles. We will also dive into isosceles trapezoids, understanding their congruent legs and the significance of their diagonal properties. Additionally, discover how to work with the median of a trapezoid, which connects the midpoints of the legs. Engage with practical problems to reinforce your understanding of these concepts!

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Understanding Trapezoids: Properties, Medians, and Isosceles Forms

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  1. 8.6 Trapezoids What you’ll learn: To recognize and apply the properties of trapezoids. Solve problems involving the medians of trapezoids.

  2. Trapezoids Trapezoids – a quadrilateral with exactly 1 pair of parallel lines. Bases – the parallel sides Legs – the nonparallel sides Base angles – formed by a leg and a base base leg leg base Base angles Base angles

  3. Isosceles Trapezoids A B Isosceles trapezoid – a trapezoid with congruent legs. Theorem 8.18 – Both pairs of base angles of an isosceles trapezoid are congruent. AB, CD Theorem 8.19 – The diagonals of an isosceles trapezoid are congruent. AD=BC C D

  4. Medians of Trapezoids Median of a trapezoid – the segment that joins the midpoints of the legs of any trapezoid. Theorem 8.20, the median of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases.

  5. ABCD is a quadrilateral with vertices A(5,1), B(-3,-1), C(-2,3), D(2,4) • Is ABCD also a trapezoid? • If it’s a trapezoid, is it an isosceles trapezoid?

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

  7. Homeworkp. 44210-32 even44-50 even

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