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

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

Definitions 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

Theorem 6.19: If a trapezoid is _______________, then each __________ of __________ angles is _______________ Theorem 6.20: If a trapezoid has a __________ of congruent __________ angles, then it is an _______________ trapezoid Theorem 6.21: A trapezoid is _______________ if and only if its _______________ are congruent Trapezoid Theorems

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

EX 1: Find the value of x A) B) P x S 10.5 M N Q 12 R P 8x - 12 S

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

Theorem 6.22: If a quadrilateral is a __________, then its ____________ are ____________________ Theorem 6.23: If a quadrilateral is a __________, then exactly __________ pair of ____________ angles are _______________ Kite Theorems

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