From a Parallelogram to a Rhombus - Examples, Exercises and Solutions

Given the parallelogram:

Is this parallelogram a rhombus?

The definition of a rhombus is "a quadrilateral with all sides equal"

Therefore, the square in the diagram is indeed a rhombus

Thus, the correct answer is answer A.

True

Look at the parallelogram below:

The diagonals form 90 degrees at the center of the parallelogram.

Is this parallelogram a rhombus?

The parallelogram whose diagonals are perpendicular to each other (meaning the angle between them is $90\degree$) is a rhombus, therefore the given parallelogram is a rhombus.

Therefore, the correct answer is answer A.

Yes.

Given the parallelogram:

Is this parallelogram a rhombus?

Not true

Given the parallelogram:

Is this parallelogram a rhombus?

True

Look at the parallelogram below:

The diagonals form 2 pairs of different angles at the center of the parallelogram.

Is the parallelogram a rhombus?

No.

Given the parallelogram:

Is this parallelogram a rhombus?

Not true

Is this parallelogram necessarily a rhombus?

Yes

Is this parallelogram necessarily a rhombus?

No