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. 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

4. 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

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

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

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

8. 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

9. 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