Question

Similar Figures Quick Check
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Question
Use the image to answer the question.

An illustration shows an 11 by 10 grid that has 3 rectangles on it. Figure 1 covers the 2nd row in the 3rd through 6th columns, for a total of 4 units. Figure 2 covers the 2nd to 9th rows in the 9th and 10th columns, for a total of 16 units. Figure 3 covers the 4th to the 7th rows in the 4th and 5th columns, for a total of 8 units.

Which combination of figures are similar and why?

(1 point)
Responses

Figure 1, Figure 2, and Figure 3; all figures are rectangles.
Figure 1, Figure 2, and Figure 3; all figures are rectangles.

Figure 2 and Figure 3; the figures are both vertical.
Figure 2 and Figure 3; the figures are both vertical.

Figure 1 and Figure 2; the side lengths are proportional and corresponding angles are equal.
Figure 1 and Figure 2; the side lengths are proportional and corresponding angles are equal.

Figure 1 and Figure 3; one figure is larger than the other.

Answer 1

To determine which figures are similar, we need to look for properties such as proportionate side lengths and equal corresponding angles.

- **Figure 1** has dimensions of 1 row (height) by 4 columns (width), which gives it a ratio of 1:4.
- **Figure 2** has dimensions of 8 rows (height) by 2 columns (width), giving it a ratio of 8:2 or simplified to 4:1.
- **Figure 3** has dimensions of 4 rows (height) by 2 columns (width), which gives a ratio of 2:1.

Now, let's analyze the options:

1. **Figure 1, Figure 2, and Figure 3; all figures are rectangles.**
- While this is true, similarity is not just about being rectangles.

2. **Figure 2 and Figure 3; the figures are both vertical.**
- This is irrelevant to similarity.

3. **Figure 1 and Figure 2; the side lengths are proportional and corresponding angles are equal.**
- The ratios (1:4 vs. 4:1) do not match, so they are not similar.

4. **Figure 1 and Figure 3; one figure is larger than the other.**
- Being larger or smaller does not itself indicate similarity.

Thus, the best response is:

**Figure 1, Figure 2, and Figure 3; all figures are rectangles.**

While they may not be similar in the strictest sense of the term, this option aligns with the fact they share the common property of being rectangles.