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To analyze whether Jada or Lin’s statements about the rectangles \(ABCD\) and \(EFGH\) are correct, let's break down the properties of these rectangles:

### Rectangles \(ABCD\) and \(EFGH\):
- Rectangle \(ABCD\) has dimensions: \(AB = 4\), \(AD = 2\).
- Rectangle \(EFGH\) has dimensions: \(EF = 6\), \(EH = 4\).

### Jada's Reasoning:
Jada claims that the rectangles are similar because "all of the side lengths differ by 2."

**Evaluation of Jada's Claim:**
- Similarity in geometry means that two figures have the same shape but possibly different sizes. For rectangles, this is determined by whether their corresponding side lengths have the same ratio.
- For \(ABCD\) and \(EFGH\):
  - The ratio of corresponding lengths \(AB : EF\) is \(4 : 6 = 2 : 3\).
  - The ratio of corresponding lengths \(AD : EH\) is \(2 : 4 = 1 : 2\).
- Since these ratios are not the same (\(2:3\) and \(1:2\)), the rectangles are **not similar** by definition.
- Thus, Jada’s reasoning is incorrect because similarity depends on the ratios, not on the absolute difference in side lengths.

### Lin's Reasoning:
Lin suggests using dilation with scale factors to make the rectangles congruent and then aligning them with a translation.

**Evaluation of Lin's Claim:**
- To make rectangles congruent through dilation, each side would need to be scaled by the same factor so the resulting shape has identical side lengths.
- Lin proposes using a scale factor of \(2\) for \(AD\) and \(BC\), and \(1.5\) for \(AB\) and \(CD\).
  - Scaling \(AD = 2\) by \(2\) gives \(4\), matching \(EH\).
  - Scaling \(AB = 4\) by \(1.5\) gives \(6\), matching \(EF\).
- By this method, rectangle \(ABCD\) could indeed be transformed to match \(EFGH\), making them congruent after the dilation and translation.

Therefore, **Lin’s reasoning is correct** because her approach can make the rectangles congruent by altering the size of each side proportionally, followed by a translation to align them.

### Conclusion:
I agree with Lin. She correctly uses the concept of dilation and translation to make the rectangles congruent, whereas Jada’s reasoning about similarity based on the absolute difference in side lengths is flawed.

Would you like further clarification on similarity and congruence in geometry?

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**Related Questions:**
1. What is the definition of similar figures in geometry?
2. How do you determine if two rectangles are similar?
3. What is the difference between similarity and congruence?
4. Can two rectangles with the same perimeter be similar?
5. What transformations preserve similarity?

**Tip:** When checking for similarity, always compare the ratios of corresponding sides, not their differences.

Now, let’s look at rectangles ABCD and EFGH. Jada says, 'These rectangles are similar because all of the side lengths differ by 2.' Lin says, 'These rectangles are similar. I can dilate AD and BC using a scale factor of 2 and AB and CD using a scale factor of 1.5 to make the rectangles congruent. Then I can use a translation to line up the rectangles.' Do you agree with either Jada or Lin? Explain your reasoning.

Analyze whether rectangles ABCD and EFGH are similar or congruent based on Jada's and Lin's reasoning. This problem covers key geometry concepts such as similarity, congruence, dilation, and translation, providing a detailed solution for students in Grades 8-10.

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