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:

• Option 1: In a parallelogram, if the diagonals are equal, it is a rectangle. This is a property of rectangles.
• Option 2: In a parallelogram, both pairs of opposite sides are congruent by definition. This does not specifically prove it is a rectangle.
• Option 3: In a rhombus, the diagonals are perpendicular. This is not a property of rectangles.
• Option 4: In a parallelogram, the diagonals bisect each other by definition. This does not specifically prove it is a rectangle.
• Option 5: In a parallelogram, if adjacent sides are perpendicular (slopes of adjacent sides multiply to - 1), then 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.