https://file.aiquickdraw.com/mathbot/file/1728361247141nehdl12u.jpg

Let's analyze the problem one step at a time. We need to determine whether the given figures are rectangles, rhombuses, or squares based on the information provided.

### Figure 1:
- **Given Information:** \( PQ = QR \)
- **Reasoning:** The figure is a quadrilateral, and two adjacent sides are congruent, suggesting it could be a rhombus. To confirm it’s a rhombus, we would need all sides to be equal. Since adjacent sides are congruent, this strongly suggests that the figure is a **rhombus**.

### Figure 2:
- **Given Information:** \( \text{m} \angle D = 90^\circ \)
- **Reasoning:** One of the interior angles is \( 90^\circ \), meaning the figure could either be a rectangle or square. However, there is no indication that all sides are equal, so the best conclusion is that this figure is a **rectangle**.

### Figure 3:
- **Given Information:** \( QS \perp TR \), \( TQ = QR \)
- **Reasoning:** The diagonals are perpendicular, which is a property of both rhombuses and squares. Additionally, two adjacent sides are congruent. Since the diagonals of a square are perpendicular and all sides are equal, this indicates the figure is a **square**.

### Summary of answers:
1. Rhombus
2. Rectangle
3. Square

Would you like any details or further explanation on any part of the reasoning?

### Related Questions:
1. How do you differentiate between a rhombus and a square geometrically?
2. Why does a rectangle have to have all right angles?
3. What other properties of diagonals help in identifying squares or rhombuses?
4. Can a square also be classified as a rhombus? Why or why not?
5. How can you use side lengths to verify if a figure is a square or a rhombus?

### Tip:
When dealing with quadrilaterals, always check for both side lengths and angle measures—especially perpendicular diagonals or congruent sides—to determine the exact type of figure.

State whether the figure is a rectangle, rhombus, or square. Explain your reasoning. There may be more than 1 answer.

This problem involves classifying shapes as either a rectangle, rhombus, or square. Analyze each quadrilateral based on the given properties like side lengths, angles, and diagonals. Suitable for Grades 6-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation