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Exploring Trapezoids and Kites in Geometry

Discover the properties and theorems related to trapezoids and kites. Learn to identify shapes and calculate angles and sides effectively.

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Exploring Trapezoids and Kites in Geometry

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  1. Section 6.5 Trapezoids and Kites OBJECTIVE: To verify and use properties of trapezoids and kites BIG IDEA: Reasoning and Proof ESSENTIAL UNDERSTANDING: The angles, sides and diagonals of a trapezoid have certain properties. MATHEMATICAL PRACTICE: Attend to precision

  2. Trapezoid: a quadrilateral with ____________ one __________ of parallel sides • The parallel sides of a trapezoid are called ___________ • The nonparallel sides are called ____________ • The two angles that share a base of a trapezoid are called _______________ _______________. A trapezoid has two pairs of base angles. Definition

  3. Isosceles Trapezoid: a trapezoid with ______________ legs • Midsegment of a trapezoid: a segment that _______________ the ____________________ of the legs of a trapezoid. • Kite: a quadrilateral that has __________ pairs of _______________ congruent __________, but ____________ sides are not congruent Definitions

  4. Theorem 6.14: If a trapezoid is _______________, then each __________ of __________ angles is _______________ • Theorem 6.15: If a trapezoid has a __________ of congruent __________ angles, then it is an _______________ trapezoid • Theorem 6.16: A trapezoid is _______________ if and only if its _______________ are congruent Trapezoid Theorems

  5. Midsegment Theorem for Trapezoids: The _______________ of a trapezoid is ____________ to each __________ and its length is _____ ________ the ________ of the lengths of the ____________ Trapezoid Theorem

  6. A) • B) P x S 10.5 M N Q 12 R P 8x - 12 S 2x + 11 M N Q 10 R EX 1: Find the value of x

  7. C) • D) Q R S P J M K L EX 2: Find the measure of all the angles

  8. Theorem 6.18: If a quadrilateral is a __________, then its ____________ are ____________________ • Theorem 6.19: If a quadrilateral is a __________, then exactly __________ pair of ____________ angles are _______________ Kite Theorems

  9. A) • B) • C) Find the measure of the angles A, B and C EX 3: Find the value of x

  10. 6.5 p. 35910 – 15 all, 16 – 24 evens, 21, 28 – 32 evens, 36, 38, 48, 50, 51, 52, 58, 60, 62 24 questions

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