Question

A parallelogram has four angles that are the same measure. Is it a square?

Choose Yes or No to tell if the answer and explanation is correct.
Yes. Only squares have four angles that are the same measure.

Yes. It could be a square if all sides are also the same measure.

No. If the sides are not the same length, it is not a square.

No. The figure is a rhombus.

Answer 1

Not all parallelograms with four equal angles are squares; they need equal sides and right angles to be considered squares. Otherwise, they could be rectangles or rhombuses, depending on the side lengths and angles.

Step-by-step explanation:

A parallelogram with four angles of the same measure could potentially be a square, but this is not guaranteed unless all its sides are also of equal length and the angles are right angles (90 degrees each). If a parallelogram has equal angles but the sides are not equal, then it is not a square but could be a rectangle. On the other hand, if a parallelogram has sides of the same length but the angles are not right angles, it is called a rhombus. As in the case with similar figures, the ratio of areas of similar figures is the square of the scale factor, meaning that if the side of one square is twice as long as the side of another square, the area of the larger square will be four times larger than the area of the smaller square.