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:

• For the first option: In a parallelogram, if the diagonals are equal, it is a rectangle. This is a well - known property of rectangles.
• For the second option: In a parallelogram, both pairs of opposite sides are already congruent. This is a property of parallelograms in general, not specific to rectangles.
• For the third option: If the diagonals of a parallelogram are perpendicular, it is a rhombus, not a rectangle.
• For the fourth option: In a parallelogram, the diagonals already bisect each other. This is a general property of parallelograms, not specific to rectangles.
• For the fifth option: In a parallelogram, if adjacent sides are perpendicular (i.e., the slopes of adjacent sides multiply to - 1), then all angles are right angles, and it is a rectangle.

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.