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## Trapezoids and Kites

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**Trapezoids and Kites**Notes 24 – Section 6.6**Essential Learnings**• Students will understand and be able to recognize and apply the properties of trapezoids and kites.**Trapezoid**• A trapezoid is a quadrilateral with exactly one pair of parallel sides. Base Leg Leg Base**Isosceles Trapezoid**• If the legs of a trapezoid are congruent then it is an isosceles trapezoid. Base Leg Leg Base**Isosceles Trapezoids**• If a trapezoid is isosceles, then each pair of base angles is congruent. A B D C**Isosceles Trapezoids**• If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid. A B D C**Isosceles Trapezoids**• A trapezoid is isosceles if and only if its diagonals are congruent. A B D C**Example 1**JKLM is an isosceles trapezoid. Find m∠K and x. J K 2x 14 112º L M**Midsegment of a Trapezoid**• The midsegment of a trapezoid is a segment that connects the midpoints of the legs of the trapezoid.**Trapezoid Midsegment Theorem**• The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. x m y**Example 2**For trapezoid JKLM, P and Q are midpoints of the legs. If JK = 18 and PQ = 28, find LM. J K P Q M L**Kite**• A kite is a quadrilateral with exactly two pairs of consecutive congruent sides.**Kites**• If a quadrilateral is a kite, then its diagonals are perpendicular. • One diagonal is bisected. B A C D**Kites**• If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.**Example 3**If WXYZ is a kite, find m∠XYZ. W Z 48º 110º X Y**Example 4**If MNPQ is a kite, find NP. P 4 N Q 7 11 M**Example 5**If m∠WXY = 72, m∠WZY = 4x and m∠ZWX = 10x, find m∠ZYX. W U Z X Y**Assignment**Pages 440-442: 8-11, 17, 19, 21, 26, 27, 35-39, 41, 43, 49, 50, 53-57 Unit Study Guide 4 – Due Monday (12/10)