To determine which of the rectangles (A, B, C, D) are similar, we need to check the aspect ratios of each rectangle. Rectangles are considered similar if their corresponding side lengths are proportional, which means they must have the same aspect ratio (ratio of width to height).

Let's examine each rectangle's dimensions:

• Rectangle A has 4 columns and 3 rows, so its dimensions are $4 \times 3$.
• Rectangle B has 2 columns and 3 rows, so its dimensions are $2 \times 3$.
• Rectangle C has 1 column and 2 rows, so its dimensions are $1 \times 2$.
• Rectangle D has 3 columns and 2 rows, so its dimensions are $3 \times 2$.

Now, calculate the aspect ratios:

• A: $\frac{4}{3}$
• B: $\frac{2}{3}$
• C: $\frac{1}{2}$
• D: $\frac{3}{2}$

Comparison of aspect ratios:

• Rectangles A and B have different aspect ratios ($\frac{4}{3} \neq \frac{2}{3}$).
• Rectangles B and C have different aspect ratios ($\frac{2}{3} \neq \frac{1}{2}$).
• Rectangles C and D have different aspect ratios ($\frac{1}{2} \neq \frac{3}{2}$).
• Rectangles A and D have the same aspect ratio ($\frac{4}{3} = \frac{3}{2}$) if the orientation of D is considered to be rotated.

Thus, Rectangles A and D are similar because they share the same aspect ratio, meaning their corresponding sides are proportional, albeit rotated.

Would you like more details or have any questions?

Related Questions:

1. How do we formally define the concept of similarity for shapes like rectangles?
2. What is the significance of aspect ratio in geometry?
3. Could the orientation of a shape affect its similarity classification?
4. How do we calculate the scale factor between two similar rectangles?
5. Can other shapes besides rectangles also be compared for similarity using aspect ratios?

Tip: When checking similarity, always compare the ratios of corresponding sides, not just the absolute lengths.