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The question in the image asks about a parallelogram \( ABCD \), where each of the four angles shown is \( 66^\circ \). The options for classifying the parallelogram as a rectangle, square, or rhombus based on the given angles are provided.

### Let's analyze the situation:

1. **Given the angles**: The interior angles of the parallelogram are \( 66^\circ \). In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum up to \( 180^\circ \)).
   - In this case, the adjacent angles are not \( 90^\circ \), so the figure cannot be a **rectangle** or a **square**, because both of these figures have all angles equal to \( 90^\circ \).
   
2. **Rhombus properties**: A rhombus is a type of parallelogram where all sides are equal in length, and the diagonals bisect the angles.
   - In the diagram, the diagonal divides the parallelogram into two equal halves, bisecting the angles, which is a defining property of a rhombus. This suggests that the parallelogram could be a **rhombus**.

### Conclusion:
The correct answer is:
- **"Parallelogram \( ABCD \) is a rhombus, because the diagonal bisects two angles."**

The other options do not fit, as the angle measures do not indicate a rectangle or square.

Would you like more detailed information or clarification on this?

Here are some related questions you could consider:
1. How can you determine if a parallelogram is a rhombus just by its diagonals?
2. What are the main differences between a square, rectangle, and rhombus?
3. How does the property of diagonals in a rhombus help in angle bisection?
4. Can a parallelogram with unequal angles still be a rectangle or square?
5. What geometric properties make all sides of a rhombus equal?

### Tip:
Remember that a rhombus is always a parallelogram, but not every parallelogram is a rhombus. The defining feature of a rhombus is that all sides are equal, and diagonals bisect the interior angles.

Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain.

Explore the geometric properties of parallelogram ABCD with angles of 66°. Determine whether it can be classified as a rhombus, rectangle, or square based on angle bisection and supplementary angles in parallelograms. This problem is suited for students in grades 8-10.

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