Coordinate Plane Proofs

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. 

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. 

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

Explain why it is convenient to place a right triangle on the grid as shown when writing a coordinate proof.

• The hypotenuse of the right triangle is easy to identify.

• The side lengths are often easier to find because you are using zeros in your expressions.

• It is easier to dilate the figure on the coordinate plane.

• Both legs have the same length when you place the triangle on the x- and y-axes.

Explain why it is convenient to place a right triangle on the grid as shown when writing a coordinate proof.

• The hypotenuse of the right triangle is easy to identify.

• The side lengths are often easier to find because you are using zeros in your expressions.

• It is easier to dilate the figure on the coordinate plane.

• Both legs have the same length when you place the triangle on the x- and y-axes.

Complete the coordinate proof of the theorem.
Given: ABCD is a square.
Prove: The diagonals of ​ ABCD ​ are perpendicular.
The coordinates of square ABCD A(0, 0), B(____, 0), C(_____, a), and ​ D(0, a).

• 5 , 4

• a, a

• 1 , -1

• a, 1

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 AB is congruent to side BC.

• Yes they are congruent

• No, they are not congruent