Parallelogram Coordinate Proofs

How would you prove that the diagonals of a parallelogram bisect each other?

• Slope

• Distance Formula

• Midpoint

• Guess

How would you prove the opposite sides of a parallelogram are parallel?

• Slope

• Distance Formula

• Midpoint

Analyze the graph. How can you prove this is a rhombus using slope?

• Yes, because AC has a slope that is undefined and BD has a slope of 0

• No, because AC has a slope of 0 and BD has a slope of 0

• Yes, because AC has a slope of 0 and BD has a slope that is undefined

• No, because AC and BD have undefined slopes

Julia proved ABCD is a parallelogram. She notices that side AB has a slope of 8/3 and BC has a slope of 1/3. What can she classify ABCD as?

• A rectangle

• A square

• A rhombus

• Just a parallelogram

What is reason #3? Make sure you write-in the reasons on your proofs.

• Definition of a parallelogram

• Definition of a quadrilateral

• opposite sides are congruent property

• opposite sides are supplementary

Fill in the Reason.

• Opposite sides of a parallelogram are congruent.

• definition of parallelogram

• Prove

• CPCTC

Fill in the Reason

• Opposite sides of a parallelogram are congruent.

• definition of parallelogram

• Prove

• CPCTC

You have plotted the parallelogram in the picture. Which sides would you want to find the slope of first?

• AB and BC

• AB and AD

• AD and DC

• AB and DC

You have plotted the parallelogram in the picture. What is the slope of line BC without having to use the slope formula?

• 0

• Undefined

Brad proved that ABCD is a parallelogram by proving both sets of opposite sides to be parallel. What should he do next if he wants to prove it is a rhombus?

• Find the distance of each line to see if they are congruent. 

• Compare the slopes of adjacent sides to see if they are perpendicular.