# From Parallelogram to Square

## First step

To demonstrate that the parallelogram is a square, we must first prove that it is a rectangle or a rhombus.

### How can we prove that a parallelogram is a rectangle?

Showing that at least one of the following conditions is met:

1. If the diagonals of the parallelogram are identical, it means that it is a rectangle.
2. If the parallelogram has an angle of 90 degrees, it means that it is a rectangle.

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### How can we prove that a parallelogram is a rhombus?

Showing that at least one of the following conditions is met:

1. If the parallelogram has a pair of equal adjacent sides, it is a rhombus.
2. If the diagonals of the parallelogram are bisectors, it is a rhombus.
3. If the diagonals of the parallelogram are perpendicular and form a 90º angle, it is a rhombus.

Observe, you should not prove that the parallelogram is both a rectangle and a rhombus.
Check which figures (rectangle or rhombus) you can prove exist in the following parallelogram, then proceed to the second step.

## Second step

Now, we must demonstrate that the rectangle or rhombus before us is a square.
The second step is divided into two parts.

### If we have proven that the parallelogram is a rectangle

We can demonstrate that the rectangle is a square when at least one of the following conditions is met:

1. If there is a pair of adjacent sides that are equal, it is a square.
2. If the diagonals of the rectangle are perpendicular (form a 90-degree angle), it is a square.
3. If the diagonals of the rectangle are bisectors, it is a square.

### If we have demonstrated that the parallelogram is a rhombus

We can prove that a rhombus is a square when at least one of the following conditions is met:

1. If the rhombus has a right angle (90º), it is a square.
2. If the diagonals of the rhombus are equal, it is a square.

Conclusion:
You will be able to prove that a parallelogram is a square if you first prove that it is a rectangle or a rhombus.
After you prove that the parallelogram is a rectangle or a rhombus, you will prove that said figure is a square.

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