https://file.aiquickdraw.com/mathbot/file/1725485013679yzjbu85h.jpg

The problem presented in the image deals with an indirect proof that Alexa is trying to construct regarding the relationship between rectangles and squares.

### Summary of the Problem:
1. **Initial Assumption (Indirect Proof Setup):**
   Alexa begins by assuming the opposite of what she wants to prove. She assumes that *all rectangles are squares*.

2. **Counterexample:**
   Alexa presents a counterexample of a non-square rectangle (parallelogram-like shape) to disprove the assumption that "all rectangles are squares."

3. **Conclusion:**
   From the counterexample, she concludes that not all rectangles are squares.

### Question:
The question asks, "Which statement best describes Alexa’s indirect proof?" and provides the following options:
- A) Alexa’s proof is correct and contains no errors.
- B) Alexa’s proof is incorrect. She made an error in her counterexample.
- C) Alexa’s proof is incorrect. She made an error in her assumption.
- D) Alexa’s proof is incorrect. She followed the steps of an indirect proof in the wrong order.

### Solution:
- **Option A (Correct Proof)**: This option suggests that Alexa's proof is correct. The method she follows aligns with an indirect proof structure: she assumes the opposite (that all rectangles are squares), provides a counterexample of a non-square rectangle, and concludes that the assumption is false. Therefore, her proof process is correct.
- **Option B (Error in Counterexample)**: This is not the case because the counterexample correctly shows that not all rectangles are squares.
- **Option C (Error in Assumption)**: There is no error in assuming the opposite in an indirect proof. This is a standard technique.
- **Option D (Wrong Order)**: Alexa follows the correct order of steps in an indirect proof.

Thus, **Option A** is the correct answer: "Alexa’s proof is correct and contains no errors."

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Do you have any questions or need further clarification?

### Follow-up questions:
1. What is the structure of an indirect proof?
2. Why is Alexa's assumption important for her proof?
3. How does a counterexample disprove a universal assumption?
4. Can indirect proof be applied to other geometrical statements?
5. What are some other common methods of mathematical proof?

**Tip:** Always ensure that your counterexample directly contradicts the assumption you're trying to disprove in an indirect proof.

Alexa wants to use an indirect proof to prove that all rectangles are not squares. She first assumes that all rectangles are squares. Alexa then presents the following counterexample to disprove her assumption. She concludes that all rectangles must not be squares. Which statement best describes Alexa's indirect proof?

Learn how Alexa uses an indirect proof to disprove the assumption that all rectangles are squares. Explore the process of using counterexamples to show that not all rectangles must be squares in this high school-level geometry problem.

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