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Trapezoids and Kites 1/16/13 Mrs. B

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Objectives: Use properties of trapezoids. Use properties of kites.

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Using properties of trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel sides called bases. A trapezoid has two pairs of base angles. Ex. D and C And A and B. The nonparallel sides are the legs of the trapezoid.

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Using properties of trapezoids If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

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Isosceles Trapezoid If a trapezoid is isosceles, then each pair of base angles is congruent. A B, C D

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Isosceles Trapezoid If a trapezoid is isosceles, then adjacent angles (not bases) are supplementary.

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Ex. 1: Using properties of Isosceles Trapezoids Given, angle X is 50 Find

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Isosceles Trapezoid A trapezoid is isosceles if and only if its diagonals are congruent. ABCD is isosceles if and only if AC BD.

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Midsegment of a trapezoid The midsegment of a trapezoid is the segment that connects the midpoints of its legs.

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Theorem 6.17: Midsegment of a trapezoid The midsegment of a trapezoid is parallel to each base and its length is one half the sums of the lengths of the bases. MN AD, MNBC MN = ½ (AD + BC)

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Ex. 3: Finding Midsegment lengths of trapezoids LAYER CAKE A baker is making a cake like the one at the right. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer be?

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Ex. 3: Finding Midsegment lengths of trapezoids Use the midsegment theorem for trapezoids. DG = ½(EF + CH)= ½ (8 + 20) = 14 C D E D G F

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Using properties of kites A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.

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Kite theorems Theorem 6.18 If a quadrilateral is a kite, then its diagonals are perpendicular. AC BD

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Kite theorems Theorem 6.19 If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent. A C B not = D

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Ex. 4: Using the diagonals of a kite WXYZ is a kite so the diagonals are perpendicular. You can use the Pythagorean Theorem to find the side lengths. WX = XY =

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Ex. 5: Angles of a kite Find m G and m J in the diagram. 132 ° 60 °

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