Bell work: What geometric name(s) could you give each polygon? What properties/characteristics do you observe for each polygon?

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 for Toolkit Definition – a quadrilateral with 2 pairs of parallel sides Turn to core book page 246 Theorem 1 – opposite sides of a parallelogram are congruent Theorem 2 – opposite angles are congruent

Parallel Notes Continued: Theorem 3 – consecutive angles of a parallelogram are supplementary Theorem 4 – diagonals of a parallelogram bisect each other

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

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

EX 4: Use a system of equations to find the LN and KM.

EX 5: 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 Core Book Standard:  Pg 249 ALL  Pg 251 #2, 7, 10, 12, 14  Pg 252 #2, 3 Honors:  Pg 249 ALL  Pg 251 #7, 9, 10, 14, 15  Pg 252 #2, 3 You have 20 minutes to start it. Whatever you don’t finish is homework. Due Wednesday.

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

EX 1: Is there enough information to prove the quadrilateral is a parallelogram? Explain.

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

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

6-3 classwork Core book pg 255 #1 – 5 There will be no additional homework given for chapter 6 so that you can focus on your quarter project!