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.