Trapezoids Trapezoid - A quadrilateral with exactly one pair of parallel sides. Bases - The parallel sides of a trapezoid. Legs - The nonparallel sides.

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Presentation transcript:

Trapezoids Trapezoid - A quadrilateral with exactly one pair of parallel sides. Bases - The parallel sides of a trapezoid. Legs - The nonparallel sides of a trapezoid. Base angles - The angles formed by a base and one of the legs.

Trapezoids Isosceles trapezoid - A trapezoid with congruent legs. Theorem 8.18 Both pairs of base angles of an isosceles trapezoid are congruent. Theorem 8.19 The diagonals of an isosceles trapezoid are congruent.

Example 6-2b The sides of a picture frame appear to be two adjacent trapezoids. Determine if they are isosceles trapezoids. Answer: yes

Example 6-3e Answer: Exactly one pair of opposite sides is parallel. Therefore, QRST is a trapezoid. QRST is a quadrilateral with vertices Q(–3, –2), R(–2, 2), S(1, 4), and T(6, 4). a. Verify that QRST is a trapezoid. Answer: Since the legs are not congruent, QRST is not an isosceles trapezoid. b.Determine whether QRST is an isosceles trapezoid. Explain.

Trapezoids Median of a trapezoid - A segment that joins the midpoints of the legs of the trapezoid. Theorem 8.20 The median of a trapezoid is parallel to the bases and has a length equal to half the sum of the lengths of the bases.

Example 6-4e WXYZ is an isosceles trapezoid with median Answer: a. b. Answer: Because