Proving Parallelograms: Coordinate Geometry Unit 1C3 Day 4
Do Now For two points in a coordinate plane, (x 1, y 1 ) and (x 2, y 2 )… What is the distance formula? What is the slope formula? What is the midpoint formula?
Using Coordinate Geometry When a figure is in the coordinate plane, you can use the ________________________ to prove that sides are congruent. You can use the _____________________ to prove sides are parallel.
Ex. 1: Using properties of parallelograms Show that A(2, -1), B(1, 3), C(6, 5) and D(7,1) are the vertices of a parallelogram.
Ex. 1a: Using properties of parallelograms Method 1—Show that opposite sides have the same slope, so they are parallel.
Ex. 1b: Using properties of parallelograms Method 2—Show that opposite sides have the same length.
Ex. 1c: Using properties of parallelograms Method 3—Show that one pair of opposite sides is congruent and parallel.
Ex. 1d: Using properties of parallelograms Method d— Show that diagonals bisect each other.
Ex. 2: Proving Parallelograms
Closure Could a hexagon with opposite sides parallel be called a parallelogram? Explain.