Coordinate Proof of Parallelograms

Brad proved that ABCD is a parallelogram and that all sides had the same distance What should he do next if he wants to prove it is a square?

• He doesn't need to do anything else, it looks like a square so he is all set. 

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

Drew used the distance formula and found each side to have a distance of 4. What does that mean?

• Side AB and AD are parallel

• Side AB and AD form a right angle

• Side AB and AD are congruent

• Nothing Specific

The slope of side AB is -3 and the slope of DC is -3. What does this mean?

• Side AB and AD are parallel

• Side AB and AD form a right angle

• Side AB and AD are congruent

• Nothing Specific

Julia proved ETNU is a parallelogram. She notices that side ET has a slope of 1/2 and EN has a slope of -2. What can she classify ETNU as?

• A rectangle

• A square

• A rhombus

• Just a parallelogram

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

Use the distance formula to see if side BC is congruent to side AD.

• Yes they are congruent

• No, they are not congruent

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

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. 

Julia proved ETNU is a parallelogram. She notices that side ET has a slope of 1/2 and EN has a slope of -2. What does this mean?

• Side ET and EN are parallel

• Side ET and EN form a right angle

• Side ET and EN are congruent

• Nothing Specific

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

• Slope

• Distance Formula

• Midpoint