Proving Quadrilaterals Coordinate

What is the length of Side AB?

• 5

• 10

• √(17)

• √(68)

Prove that the quadrilateral with vertices at (1,2), (4,5), (7,8), and (4,11) is a parallelogram.

• The quadrilateral is a parallelogram because the sum of the opposite angles is 180 degrees.

• The quadrilateral is a parallelogram because the lengths of the opposite sides are equal.

• The quadrilateral is a parallelogram because the diagonals bisect each other.

• The quadrilateral is a parallelogram because the slopes of the opposite sides 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

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.

Find the slope of the line containing the segment with endpoints (3,4) and (7,2). Use this information to prove that the quadrilateral with vertices at (1,2), (3,4), (7,2), and (5,0) is a parallelogram.

• 1

• 5

• -0.5

• 2

Find the slope of the line containing the segment with endpoints (2,5) and (6,3). Use this information to prove that the quadrilateral with vertices at (1,2), (2,5), (6,3), and (5,0) is a parallelogram.

• The slope of the line is 1

• The slope of the line is 0

• The slope of the line is 2

• The slope of the line containing the segment with endpoints (2,5) and (6,3) is -0.5

Prove that the quadrilateral with vertices at (2,3), (4,7), (8,7), and (6,3) is a rhombus using coordinate proofs.

• The sum of the squares of the diagonals is equal to the sum of the squares of the sides, so it is a rhombus.

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

• The diagonals are perpendicular to each other, so it is a rhombus.

• The opposite angles are equal, 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.

Prove that the quadrilateral with vertices at (2,3), (4,7), (8,7), and (10,3) is a trapezoid using coordinate proofs.

• Calculate the area of the quadrilateral and show that it is not a trapezoid

• Prove that the diagonals are equal in length

• Calculate the slopes of the lines and show that they are not equal.

• Show that the opposite sides are not parallel

Use the diagonals to prove that the quadrilateral with vertices at (1,2), (3,6), (7,6), and (5,2) is a parallelogram.

• The quadrilateral is a circle.

• The quadrilateral is a triangle.

• The quadrilateral is a parallelogram.

• The quadrilateral is a square.