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6.5 Trapezoids and Kites

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**Trapezoids-Some Definitions**

A trapezoid is a quadrilateral with exactly one pair of opposite sides parallel. One pair of base angles base leg leg base Second pair of base angles The parallel sides are the bases. The nonparallel sides are the legs. Base Angles come in pairs and lie along each of the bases.

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**Definition of Isosceles Trapezoid**

An isosceles trapezoid is a trapezoid with congruent legs.

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**Definition of Midsegment**

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

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**Isosceles Trapezoid Theorems**

If a trapezoid is isosceles, then each pair of base angles is congruent. If a trapezoid has one pair of congruent base angles, then it is isosceles. A trapezoid is isosceles if and only if its diagonals are congruent.

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**Midsegment of a Trapezoid Theorem**

The midsegment of a trapezoid is parallel to each base and half the sum of the lengths of the bases. x y z

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Definition of a Kite A kite is a quadrilateral with two pairs of consecutive sides congruent.

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Kite Theorems If a quadrilateral is a kite, then its diagonals are perpendicular. If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.

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Examples 1.

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4. A potter crafts a trapezoidal relish dish, placing a divider in the middle of the dish. How long must the divider be to ensure that it divides the legs in half?

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5. HP=

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**6. Find the measures of all the angles.**

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Find the value of x. x

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Find the value of x.

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