Properties of Parallelograms Objective: Students will be able to prove and apply new properties of parallelograms to solve problems.

Parallelogram What else do we know about parallelograms because of the definition, could you prove it Consecutive angles supplementary – SSI Opposite sides congruent – Prove Triangles CPCTC Opposite angles congruent – CPCTC or repeated SSI property

Diagonals of a Parallelogram What do you think is special about the diagonals of a parallelogram? Are they perpendicular like a kite? Are they congruent like a trapezoid? Do they bisect each other or the angles? Diagonals Bisect Each other

Remember Parallel Line Properties Corresponding - congruent Alternate interior – congruent Same Side Interior - Supplementary

Proof Given: ABCE is a parallelogram Prove: diagonals bisect each other What triangles are you going to use? What exactly do you have to show to prove they are bisected?

Example – shapes are parallelograms

Vectors – brief examples Vector – is a quantity that has both magnitude and direction Describe velocity, acceleration and force Represent a vector by drawing an arrow Length and direction of arrow represent the magnitude and direction of the vector Resultant vector is the combination of the two vectors on a single figure (sum vector) To find the resultant vector you use the two vectors to make a parallelogram and construct the diagonal

Example How would you draw the diagonal if these are two sides of a parallelogram? 1. Construct the other sides of the parallelogram using the arrows as endpoints or 2. Draw a diagonal between arrows, bisect it and connect vertex to midpoint

Homework Pg 283 1-6 and 13 Honors 11