Section 6.5Trapezoids 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

Definition 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.

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

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

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

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

Kite Theorems 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 _______________

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

6.5 P – 15 ALL, 16 – 24 EVENS, 21, 28 – 32 EVENS, 36, 38, 48, 50, 51, 52, 58, 60, questions