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

You will be able to determine that the parallelogram is a rhombus if at least one of the following conditions is met:

1. If in the parallelogram there is a pair of adjacent equal sides - it is a rhombus.
2. If in the parallelogram the diagonals bisect each other, forming angles of $90^o$ degrees, that is, they are perpendicular - it is a rhombus.
3. If in the parallelogram one of the diagonals is the bisector - it is a rhombus.

## Examples with solutions for From a Parallelogram to a Rhombus

### Exercise #1

Given the parallelogram:

Is this parallelogram a rhombus?

### Step-by-Step Solution

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

Therefore, the square in the diagram is indeed a rhombus

True

### Exercise #2

Look at the parallelogram below:

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

Is this parallelogram a rhombus?

### Step-by-Step Solution

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.

Yes.

### Exercise #3

Given the parallelogram:

Is this parallelogram a rhombus?

Not true

### Exercise #4

Given the parallelogram:

Is this parallelogram a rhombus?

Not true

### Exercise #5

Given the parallelogram:

Is this parallelogram a rhombus?

True

### Exercise #6

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.

### Exercise #7

Is this parallelogram necessarily a rhombus?