Prove Quadrilaterals on Coordinate Grid

Which could prove that this is a parallelogram?

• Consecutive sides have opposite reciprocal slopes

• Opposite sides have the same slope

• All sides have the same length

• Diagonals have the same length

Which of the coordinates given could be the fourth point used to form a rectangle?

• (3, -6)

• (-3, -6)

• (-6, 3)

• (4, -6)

Prove that the quadrilateral with vertices at (2,3), (5,7), (8,5), and (5,1) is a parallelogram.

• Calculate the area of the quadrilateral and show that it is equal to zero.

• Calculate the slopes of the opposite sides and show that they are equal.

• Prove that the diagonals bisect each other.

• Show that the opposite angles are equal.

Prove that the quadrilateral with vertices at (1,2), (3,6), (7,6), and (5,2) is a rhombus using coordinate proofs.

• All four sides are congruent, so the quadrilateral is a rhombus.

• The opposite angles are equal, so it is a rhombus

• The diagonals are perpendicular, so it is a rhombus

• The sum of the interior angles is 360 degrees, so it is a rhombus

• Find the length of all 4 sides.

• Find the length of both diagonals.

• Find the slope of both diagonals

• Find the slope of all 4 sides.

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• Find the lengths of the diagonals.

• Find the slope of each diagonal.

• Find the midpoint of each diagonal.

• Find the midpoint of each side.

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. 

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. 

Prove that the quadrilateral with vertices at (1,2), (3,6), (7,6), and (9,2) is a trapezoid using coordinate proofs.

• The diagonals are equal in length, so the quadrilateral is a trapezoid.

• The sum of the interior angles is 360 degrees, so the quadrilateral is a trapezoid.

• All sides are equal, so the quadrilateral is a trapezoid.

• One pair of opposite sides are parallel, so the quadrilateral is a trapezoid.

Norman drew three points on a coordinate grid, as shown. If Norman draws a fourth point to form a parallelogram , which point could not be Norman's point ?

• ( 5,5 )

• ( 1,-1 )

• ( -1,3 )

• ( 2, -2 )