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Trapezoids and Kites

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  1. Trapezoids and Kites Section 8.5

  2. Trapezoid Definition • A trapezoid is a quadrilateral with exactly one pair of parallel sides. These sides are the bases.

  3. Is this a trapezoid?

  4. Definition ofIsosceles Trapezoid • If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

  5. Theorem • If a trapezoid is isosceles, then each pair of base angles is congruent.

  6. Theorem • If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

  7. Theorem • A trapezoid is isosceles if and only if its diagonals are congruent.

  8. Midsegment Definition • The midsegment connects the midpoints of the legs.

  9. Midsegment Theorem • The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the bases.

  10. Example:What is the length of MN in the diagram?

  11. Kite Definition • A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

  12. Theorem • If a quadrilateral is a kite, then its diagonals are perpendicular.

  13. Theorem • If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

  14. Example:What is the measure of angle D in the kite below?

  15. Practice • p. 546: 3-16, 18-23