Let's break down the problem step-by-step by comparing the corresponding sides of Figure A and Figure B to find the ratios and verify similarity.

Step 1: Compare Vertical Sides

• Figure A's vertical side: 2 units
• Figure B's vertical side: 4 units

Ratio of Figure A to Figure B (Vertical Sides):

• Unsimplified: $\frac{2}{4}$
• Simplified: $\frac{1}{2}$

Ratio of Figure B to Figure A (Vertical Sides):

• Unsimplified: $\frac{4}{2}$
• Simplified: $2$

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Step 2: Compare Horizontal Sides

• Figure A's horizontal side: 3 units
• Figure B's horizontal side: 6 units

Ratio of Figure A to Figure B (Horizontal Sides):

• Unsimplified: $\frac{3}{6}$
• Simplified: $\frac{1}{2}$

Ratio of Figure B to Figure A (Horizontal Sides):

• Unsimplified: $\frac{6}{3}$
• Simplified: $2$

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Step 3: Verify Similarity

Since both sets of corresponding sides have equal ratios:

• Vertical sides ratio: $\frac{1}{2}$
• Horizontal sides ratio: $\frac{1}{2}$

The two figures are similar because the corresponding side lengths are proportional.

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Step 4: Scale Factor

• To scale Figure A to the size of Figure B, multiply by $2$.
• To scale Figure B to the size of Figure A, multiply by $\frac{1}{2}$.

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Let me know if you want further details or have any questions. Here are 5 related questions:

1. What is the difference between congruence and similarity in geometry?
2. How do you calculate the area of similar figures using the scale factor?
3. What happens to the perimeter of similar figures when scaled by a certain factor?
4. Can two figures be similar if one is rotated or reflected?
5. How do you find the scale factor between two triangles?

Tip: In geometry, when dealing with similar figures, the ratio of their areas is the square of the scale factor.