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TRAPEZOIDS Recognize and apply the properties of trapezoids. Solve problems involving the medians of trapezoids. Trapezoid building blocks Text p. 439 JOHN B. CORLEY
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A trapezoid is a quadrilateral with exactly one pair of parallel sides. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY
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The base angles are formed by the base and one of the legs. The non-parallel sides are called legs. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY AB CD base leg A and B are base angles C and D are base angles
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If the legs are congruent, a trapezoid is an isosceles trapezoid. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY AB C D
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If the legs are congruent, a trapezoid is an isosceles trapezoid. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY Both pairs of base angles of an isosceles trapezoid are congruent AB C D
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If the legs are congruent, a trapezoid is an isosceles trapezoid. PROPERTIES OF TRAPEZOIDS JOHN B. CORLEY The diagonals of an isosceles trapezoid are congruent AB C D
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Example 1 Identify Trapezoids JKLM is a quadrilateral with vertices J(-18, -1), K(-6, 8), L(18, 1), and M(-18, -26). 10 8 6 4 2 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -25-20-15-10-5510152025 J K L M a.Verify that JKLM is a trapezoid b.Determine whether JKLM is an isosceles trapezoid (-18, -1) (-6, 8) (18, 1) (-18, -26)
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MEDIANS OF TRAPEZOIDS median The segment that joins the midpoints of the legs of a trapezoid is called the median. The median of a trapezoid can also be called a midsegment. AB C D
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MEDIANS OF TRAPEZOIDS AB C D THEOREM The median of a trapezoid is parallel to the bases and its measure is one half the sum of the measures of the bases. E F Example: EF = ½(AB + DC)
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Example 2 Median of a Trapezoid Q R S T X Y QRST is an isosceles trapezoid with median XY 12 34 a.Find TS if QR = 22 and XY = 15
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Example 2 Median of a Trapezoid Q R S T X Y QRST is an isosceles trapezoid with median XY 12 34 b.Find m 1, m 2, m 3, and m 4 if m 1 = 4a – 10 and m 3 = 3a + 32.5
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Kites A B C D A Kite is a quadrilateral with exactly two distinct pairs of adjacent congruent sides. In kite ABCD, diagonal BD separates the kite into two congruent triangles. Diagonal AC separates the kite into two non-congruent isosceles triangles.
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