Proving in the Coordinate Plane

You can prove both pairs of opposite sides are parallel by using the slope formula.

• True

• False

If I want to show two lines are parallel what formula do I use?

• Slope

• Distance

• Midpoint

• Pythagorean Theorm

If you are using the distance formula to prove a parallelogram in the coordinate plane, how many times do you have to do it?

• 1

• 2

• 3

• 4

If you want to prove a parallelogram in the coordinate plane using the both the slope formula and distance formula, how many times do you need to do each?

• 1

• 2

• 3

• 4

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.

How do you prove two lines are parallel?

• Use the distance formula

• Use the midpoint formula

• Use the slope formula and show the slopes are the same

• Use the slope formula and show the slopes are opposite reciprocals

If you can prove that one pair of opposite sides of a parallelogram are the same length and have the same slope, you can prove that it is a parallelogram.

• Always

• Sometimes

• Never

You can prove both pairs of opposite sides are congruent in a parallelogram using the distance formula.

• True

• False

What formula would you use to show lengths are equal?

• Slope Formula

• Distance Formula

• Midpoint Formula

If I have a parallelogram labeled ABCD and I am going to prove it using the slope formula, what sides need to be congruent?