Question

Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain.

Answer 1

No, one cannot conclude that the parallelogram is a rhombus, a rectangle, or a square

Why is the information not enough

1. No information about dimension of the sides, hence cannot conclude if the shape is a rhombus

2. No information about dimension of the sides, hence cannot conclude if the shape is a square

3. The information of bisecting each diagonal without mentioning the angle formed at the point of bisection, is not enough to conclude that the shape is a rectangle

Answer 2

Explanation:

A parallelogram is a four-sided figure with opposite sides parallel. A rhombus is a type of parallelogram with all four sides of equal length, while a rectangle is a parallelogram with four right angles. A square is a type of rectangle with all four sides of equal length.

Therefore, if a parallelogram has all four sides of equal length and its angles are all right angles, then it is a square. If a parallelogram has all four sides of equal length but not all angles are right angles, then it is a rhombus. If a parallelogram has opposite sides parallel and all angles are right angles, then it is a rectangle. If a parallelogram does not have all sides of equal length or all right angles, then it is none of the above.

To determine which of these properties a given parallelogram has, we would need additional information, such as the measurements of its sides and angles.