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:

1. In a rectangle, the diagonals are equal. Calculating diagonal lengths and showing equality verifies it could be a rectangle.
2. Showing opposite - side congruence only proves it's a parallelogram, not necessarily a rectangle.
3. Diagonals of a rectangle are not perpendicular (except in a square which is a special rectangle).
4. Diagonals bisecting each other is a property of all parallelograms, not unique to rectangles.
5. In a rectangle, adjacent sides are perpendicular. Calculating side - slopes and showing perpendicularity verifies it's 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.