https://file.aiquickdraw.com/mathbot/file/1726455040196y1wejfp2.jpg

In the image, we are asked if the parallelogram \( QRST \) is a rhombus. Let's analyze the diagram to answer this.

Key observations:
1. **Parallelogram Properties**: A parallelogram has opposite sides that are equal and parallel.
2. **Rhombus Condition**: A rhombus is a special type of parallelogram where all sides are equal in length, and the diagonals are perpendicular to each other.
3. **Given Information**: The diagonals \( QT \) and \( RS \) intersect at \( U \), and it is given that the angle formed at the intersection, \( \angle QUR \), is \( 90^\circ \).

Since the diagonals intersect at a right angle (i.e., \( 90^\circ \)), this is a key property of a rhombus. In a general parallelogram, diagonals do not necessarily meet at a right angle, but they always do in a rhombus.

Thus, **parallelogram \( QRST \) is indeed a rhombus** because:
- The diagonals are perpendicular.
  
The correct answer is **Yes**.

Would you like further details or have any questions?

Here are 5 related questions to expand this concept:
1. What are the properties of diagonals in a general parallelogram?
2. Can a parallelogram be a rhombus if its diagonals are not perpendicular?
3. What are the other conditions that can define a shape as a rhombus?
4. How does a rhombus differ from a square in terms of properties?
5. Can a parallelogram with one right angle be a rhombus?

**Tip**: Always check the diagonals for perpendicularity when identifying rhombuses, as this is a defining feature.

Analyze whether parallelogram QRST is a rhombus by looking at the perpendicular diagonals in the figure. This question explores the properties of parallelograms and rhombuses, including how perpendicular diagonals define a rhombus. Suitable for students in Grades 7-9.

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