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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. <A + <D = 180 <B + <C = 80

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**Ex. 1: Using properties of Isosceles Trapezoids**

Given, angle X is 50 Find <R, < P and <Q, 50°

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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, MN║BC 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” F D G D C

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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 mG and mJ in the diagram. 132° 60°

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