Coordinate Plane Proofs

• mBC=mCD and BC = CD

• mAB = mCD

• AB = CD, BC = AD

• mAB ∙ m BC = -1

• mAB ∙ mBC = -1

• AB = CD

• AB = BC

• mAB = mBC

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

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.

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

If you think this shape is specifically a rectangle, which of the following could prove it? (Not a parallelogram, just a rectangle.) Select all that apply (refer to your PDF document!)

• All sides are congruent

• Opposite sides are parallel

• Diagonals are congruent

• Diagonals bisect each other

• Sides are perpendicular

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

• True

• False

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.

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 )

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

• (3, -6)

• (-3, -6)

• (-6, 3)

• (4, -6)