Question

Which steps will verify that a parallelogram is a rectangle? Check all that apply.

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

Answer 1

A & E

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Answer 2

The steps that will verify that a parallelogram is a rectangle are options A and E.

What is a parallelogram?

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.

A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

Therefore, the steps that will verify that a parallelogram is a rectangle are options A and E.

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

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

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