Question

Use the diagonals to determine whether a parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a rectangle, rhombus, or square. Give all the names that apply.

Answer 1

The given parallelogram is a rectangle because its diagonals have equal lengths and bisect each other.

To determine whether the given parallelogram is a rectangle, rhombus, or square, we can use the properties of the diagonals.

A rectangle has diagonals that are equal in length and bisect each other, forming four congruent right angles. A rhombus has diagonals that are perpendicular to each other, but they are not necessarily equal in length. A square, on the other hand, has diagonals that are equal in length and bisect each other at right angles.

By calculating the lengths of the diagonals for the given parallelogram, we can determine its shape. The length of the shorter diagonal is 8 units, and the length of the longer diagonal is also 8 units. Since both diagonals have equal lengths and bisect each other, the given parallelogram is a rectangle. It is not a rhombus or a square because the diagonals are not perpendicular to each other.

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