https://file.aiquickdraw.com/mathbot/file/1726455137496dmvxnamc.jpg

In the diagram, we see a parallelogram \( GHJI \), and the question is asking whether this parallelogram is a rhombus.

### Properties of a rhombus:
1. **Equal Sides:** All sides of a rhombus are equal.
2. **Diagonal Properties:** The diagonals of a rhombus bisect each other at right angles (90°).
3. **Parallelogram Conditions:** A rhombus is a type of parallelogram, but with additional properties like equal sides and right-angled diagonals.

### Analysis of the diagram:
- The diagonals \( GJ \) and \( HI \) intersect at \( K \), forming a 90° angle at point \( K \).
- This is a key property of rhombuses because the diagonals of a rhombus always intersect at right angles.

### Conclusion:
Since the diagonals of the parallelogram intersect at a right angle, **parallelogram \( GHJI \) is a rhombus**.

So, the correct answer is **Yes**.

Would you like more details or have any other questions?

Here are 5 related questions to think about:
1. What are the other properties of a rhombus besides equal diagonals?
2. How do the properties of a rhombus differ from a square?
3. How would you prove that a quadrilateral is a parallelogram?
4. Can a parallelogram have diagonals that do not bisect each other?
5. How do you calculate the area of a rhombus using its diagonals?

**Tip:** Always check the angles formed by diagonals when identifying special types of parallelograms.

Explore whether parallelogram GHJI is a rhombus by analyzing its diagonal properties. This problem highlights key geometric concepts like rhombuses, parallelograms, and the theorem that diagonals of a rhombus bisect at right angles. Suitable for Grades 6-8.

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