Two figures are similar if they have the exact same shape and their corresponding sides are proportional. The corresponding side lengths of the two figures are related by a scale factor.
A scale factor is the constant number you can multiply any side length in one figure by to find the corresponding side length of the similar figure.
Figure A
2 vertical by 3 horizontal graph
Figure B
4 vertical units by 6 horizontal units
In this problem, you will verify that the two rectangles are similar and find the scale factor from each figure to the other. Since rectangles have two sets of equal parallel sides, we will only need to find the ratios for two sets of sides; the horizontal and vertical lengths. If these ratios are equal, the rectangles are similar.

Note: In some cases, the simplified and unsimplifed ratios may be equal.
Find the ratio:

Unsimplified:

Simplified:

Find the ratio:

Unsimplified:

Simplified:

Find the ratio:

Unsimplified:

Simplified:

Find the ratio:

Unsimplified:

Simplified:

To scale Figure A to the size of Figure B, multiply the length of each side of Figure A by the scale factor of

To scale Figure B to the size of Figure A, multiply the length of each side of Figure B by the scale factor of

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.

Two figures are similar if they have the exact same shape and their corresponding sides are proportional. The corresponding side lengths of the two figures are related by a scale factor. Figure A: 2 vertical by 3 horizontal graph. Figure B: 4 vertical units by 6 horizontal units. In this problem, you will verify that the two rectangles are similar and find the scale factor from each figure to the other. Since rectangles have two sets of equal parallel sides, we will only need to find the ratios for two sets of sides; the horizontal and vertical lengths. If these ratios are equal, the rectangles are similar.

Learn how to verify that two rectangles are similar by comparing their corresponding side lengths and finding the scale factor. This problem involves key geometry concepts such as ratios and proportionality, suitable for students in Grades 6-8.

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