To solve this problem, we need to examine the given rectangles (A, B, C, D) and determine which of them are similar. Similarity in geometry means that two shapes have the same proportions, even though they may differ in size. In the case of rectangles, two rectangles are similar if the ratio of their width to height (or length to width) is the same.

Let's proceed step by step:

1. Identify the dimensions of each rectangle:

   • A: This rectangle consists of 12 smaller squares. Its width (horizontal length) is 6 squares, and its height (vertical length) is 2 squares.
   • B: This rectangle consists of 6 smaller squares. Its width is 2 squares, and its height is 3 squares.
   • C: This rectangle consists of 2 smaller squares. Its width is 1 square, and its height is 2 squares.
   • D: This rectangle consists of 6 smaller squares. Its width is 3 squares, and its height is 2 squares.

2. Calculate the ratios (width:height) for each rectangle:

   • A: Ratio = 6:2 = 3:1
   • B: Ratio = 2:3
   • C: Ratio = 1:2
   • D: Ratio = 3:2

3. Compare the ratios to check for similarity:

   • A has a ratio of 3:1.
   • D has a ratio of 3:2, which is different from A.
   • B has a ratio of 2:3, which is different from both A and D.
   • C has a ratio of 1:2, which is also different from the others.

Since none of the other rectangles share the same width-to-height ratio with rectangle A, it means that no rectangles are similar based on this property.

Would you like further details or have any questions?

Here are five related questions for further understanding:

1. What conditions need to be met for two figures to be similar?
2. How can scaling factors help in identifying similar figures?
3. Can two shapes with different sizes be similar, and how?
4. How are proportions useful in geometry beyond identifying similarity?
5. What happens to the area of a rectangle when two similar rectangles are compared?

Tip:

When comparing shapes for similarity, always simplify the ratios to their lowest form to make comparisons easier.