If in a parallelogram if all the four angles are in the ratio `1:1:1:1` then, what type of parallelogram is this?

Answer

To solve the question, we need to determine what type of parallelogram has all four angles in the ratio of 1:1:1:1.

### Step-by-Step Solution:

1. **Understanding the Ratio of Angles**:
Since the angles are in the ratio 1:1:1:1, we can denote each angle as \( x \). Therefore, we have:
\[ \text{Angles} = x, x, x, x \]

2. **Using the Property of Parallelograms**:
In any parallelogram, the sum of all interior angles is always \( 360^\circ \). Thus, we can write the equation:
\[ x + x + x + x = 360^\circ \]
This simplifies to:
\[ 4x = 360^\circ \]

3. **Solving for \( x \)**:
To find the value of \( x \), we divide both sides of the equation by 4:
\[ x = \frac{360^\circ}{4} = 90^\circ \]

4. **Identifying the Type of Parallelogram**:
Since each angle \( x \) is \( 90^\circ \), this means all four angles of the parallelogram are right angles. A parallelogram with all right angles is defined as a rectangle.

### Conclusion:
Thus, if in a parallelogram all four angles are in the ratio \( 1:1:1:1 \), it is a **rectangle**.

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