6-2 & 6-3: Parallelograms Rigor: Use properties of parallelograms to solve equations and prove a given quadrilateral is a parallelogram. Relevance – product design

Parallelogram Notes Definition – a quadrilateral with 2 pairs of parallel sides Theorem 1 – opposite sides of a parallelogram are congruent Theorem 2 – opposite angles of a parallelogram are congruent

Parallel Notes Continued: Theorem 3 – consecutive angles of a parallelogram are supplementary Theorem 4 – diagonals of a parallelogram bisect each other Do proofs & reflection questions for examples 2 & 4 of workbook pg 246-248

Using Parallelogram Theorems Ex 1: Solve for x in the parallelograms. Then calculate the measure of each interior angle.

EX 2: Solve for the variables in the parallelogram EX 2: Solve for the variables in the parallelogram. How long is each diagonal?

EX 3: Use a system of equations to find the LN and KM.

EX 4: Coordinate Geometry Three vertices of □ABCD are A(1,-2), B(-2, 3), and D(5, -1). What are the coordinates of C?

6-2 Classwork from the Workbook Standard: Pg 251 #1 – 8, 10 – 14 Honors: Pg 251 #1 – 14

6-3 Notes: Proving a Quadrilateral is a Parallelogram If the converses of the 6-2 definitions and theorems are true, then the quadrilateral is a parallelogram.

EX 1: Is there enough information to prove the quadrilateral is a parallelogram? Explain.   No, there is not enough information to prove HIJK is a parallelogram because the opposite sides are not marked congruent.

Ex 2: For what values of x & y would the quadrilaterals be parallelograms?

Proofs from the workbook Turn to page 253 – 254 and complete proofs 1 & 2

6-3 classwork Workbook pg 255 #1 – 7

Honors: 6-2/6-3 Assignments Primary Assignment: join.quizizz.com Codes: Period 1: Period 5: Period 6: Secondary Assignment: Textbook pg 407 #9 – 14; pg 415 #17 - 22

Standard: 6-2/6-3 Assignments Primary Assignment: join.quizizz.com Codes: Period 2: Period 4: Period 7: Secondary Assignment: Textbook pg 407 #9 – 13; pg 415 #17 - 22