Subjects geometry

Figure Similarity 6D1Aa2

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1. **State the problem:** Determine which combination of figures among Figure 1, Figure 2, and Figure 3 are similar and explain why. 2. **Recall the definition of similar figures:** Two figures are similar if their corresponding angles are equal and their corresponding side lengths are proportional. 3. **Analyze the figures:** - Figure 3 is a rectangle spanning 3 squares wide and 3 squares tall (a square). - Figure 2 is a rectangle spanning 3 squares wide and 2 squares tall. - Figure 1 is a horizontal rectangle near the top-left corner (dimensions not explicitly given, but implied to be different from Figure 3). 4. **Check pairs for similarity:** - Figure 1 and Figure 2: The problem states their side lengths are proportional and corresponding angles are equal. - Figure 1 and Figure 3: One is larger than the other, but no mention of proportional sides. - Figure 2 and Figure 3: Both vertical rectangles but different side ratios (3x2 vs 3x3), so not similar. 5. **Conclusion:** The correct combination is Figure 1 and Figure 2 because their side lengths are proportional and corresponding angles are equal, satisfying the similarity criteria. **Final answer:** Figure 1 and Figure 2; the side lengths are proportional and corresponding angles are equal.