Question

Which steps will verify that a parallelogram is a rectangle?

Check all that apply.

• A. Calculate the lengths of the diagonals, and show that they are equal.
• B. Calculate the lengths of all sides, and show that both pairs of opposite sides are congruent.
• C. Calculate the slope of each diagonal, and show that the lines are perpendicular.
• D. Calculate the midpoints of each diagonal, and show the diagonals bisect each other.
• E. Calculate the slopes of every side, and show that adjacent sides are perpendicular.

Answer 1

Answer: (A), (E)

Calculate the slopes of every side, and show that adjacent sides are perpendicular.

Explanation for the correct options:

Determine the steps that verify a parallelogram is a rectangle

The property of rectangle are shown below:

• Opposite sides are equal in length.
• Opposite sides are parallel.
• The interior angles measure $90°$ each.
• Diagonals are equal in length.
• Diagonals bisect each other.
• Each of the diagonal bisects the rectangle into two congruent triangles.
• It has two lines of symmetry – a horizontal and a vertical.
• The mid-points of the four sides of a rectangle, when joined in order, form a rhombus.

Thus,

Calculate the slopes of every side, and show that adjacent sides are perpendicular.

Calculate the lengths of the diagonals, and show that they are equal.

Hence, option $\left(A\right)and\left(E\right)$ are correct.