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.

Explanation:

• A rectangle is a parallelogram with equal diagonals, so verifying equal diagonals works.
• Opposite sides congruent defines a parallelogram, not a rectangle specifically.
• Diagonals of a rectangle are not perpendicular (unless it's a square, a special case, not all rectangles).
• Diagonals bisecting each other is true for all parallelograms, not unique to rectangles.
• Adjacent sides perpendicular means all angles are right angles, which defines a rectangle from a parallelogram.

Answer:

• Calculate the lengths of the diagonals, and show that they are equal.
• Calculate the slopes of every side, and show that adjacent sides are perpendicular.