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6-6 Trapezoids and Kites

6-6 Trapezoids and Kites. Trapezoids. A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides of a trapezoid are called bases . The nonparallel sides are called legs .

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6-6 Trapezoids and Kites

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  1. 6-6 Trapezoids and Kites

  2. Trapezoids • A trapezoid is a quadrilateral with exactly one pair of parallel sides. • The parallel sides of a trapezoid are called bases. • The nonparallel sides are called legs. • The two angles that share a base of a trapezoid are called base angles. • An isosceles trapezoid has congruent legs.

  3. Isosceles Trapezoid Theorems Theorem 6-19: If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent. Theorem 6-20: If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.

  4. Finding Angle Measures is Trapezoids • What are mD, mE, and mF?

  5. What are mP, mQ, and mS?

  6. Midsegments • The midsegment of a trapezoid is the segment that joins the midpoints of its legs. Trapezoid Midsegment Theorem: If a quadrilateral is a trapezoid, then (1) the midsegment is parallel to the bases and (2) the length of the midsegment is half the sum (or the average) of the lengths of the bases.

  7. Using the Midsegment of a Trapezoid • QR is the midsegment of trapezoid LMNP. What is x?

  8.  MN is the midsegment of trapezoid PQRS. What is x? What is MN?

  9. Kites • A kite is a quadrilateral with two pairs of consecutive sides congruent and NO opposite sides congruent. Theorem 6-22: If a quadrilateral is a kite, then its diagonals are perpendicular.

  10. Finding Angle Measures in Kites • Quadrilateral DEFG is a kite. What are m1, m2, and m3?

  11. Quadrilateral KLMN is a kite. What are m1, m2, and m3?

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