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Kites & Trapezoids

Learn about trapezoids, bases, legs, base angles, isosceles trapezoids, and the properties related to medians and bases. Solve examples involving finding unknown values in trapezoids. Explore the characteristics of kites in quadrilaterals.

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Kites & Trapezoids

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  1. Kites & Trapezoids To recognize and apply the properties of trapezoids

  2. Definitions Trapezoid - Quadrilateral with exactly one pair of parallel sides Bases - the parallel sides in a trapezoid Legs - the non parallel sides Base angles - angles formed with the base and legs Isosceles trapezoid - trapezoid w/ congruent legs

  3. Theorems Isosceles Trapezoid Both pairs of base angles of an isosceles trapezoid are congruent The diagonals of an isosceles trapezoid are congruent

  4. Definition Median - segment that joins the midpt of the legs of a trapezoid AKA-midsegment Theorem The median is ll to the bases and its measure is 1/2 the sum of the measures of the bases

  5. Example G H K L J I Given trap. GHIJ w/ median KL, find x 3x - 1 10 7x + 1 KL = 1/2(GH + JI) 10 = 1/2 (3x - 1 + 7x + 1) 10 = 1/2 (10x) 10 = 5x 2 = x

  6. Example E 4x - 10 Z 13 B A 3x + 8 O I Find x given trap EZOI and median AB. 13 = 1/2(3x + 8 + 4x - 10) 13 = 1/2(7x - 2) 26 = 7x - 2 28 = 7x 4 = x

  7. A quadrilateral that has 2 pairs of consecutive congruent sides. Properties: The diagonals are perpendicular Exactly one pair of opposite angles are congruent. Kite

  8. Homework • PG 546 3 – 23 odd, 24 – 27, 32

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