Properties of Parallelograms 2 pairs of opposite sides parallel

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?

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 10, 11