Similarity & Scale Factors

Learn about similar figures, scale factors, and how to determine if shapes are similar.

8th Grade

Geometry

~45 min

🎮 Interactive Activity: Scale Factor Calculator

Calculate scale factors between similar figures!

Original: 10 units
Scaled: 15 units

🎮 Interactive Activity: Similarity Checker

Check if triangles are similar by comparing ratios!

Triangle 1: 3:4:5
Triangle 2: 6:8:10

1. What is Similarity?

📚 Similarity Definition

Two figures are similar if they have the same shape but may be different sizes. Their corresponding angles are equal and corresponding sides are proportional.

Key Properties:

• Corresponding angles are equal

• Corresponding sides are proportional (same ratio)

• Same shape, different size

2. Scale Factor

3. Similarity Criteria

4. Area and Volume Scaling

5. Real-World Applications

6. Worked Examples

7. Frequently Asked Questions

Practice Time!

Practice Quiz

Questions

Correct

Score

What does it mean for two figures to be similar?

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If a triangle is scaled by a factor of 2, what happens to its area?

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Two triangles have corresponding sides in ratio 3:5. What is the scale factor?

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Which condition proves two triangles are similar?

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If a rectangle is 4 by 6 and scaled by factor 1.5, what are the new dimensions?

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What is the scale factor if a 10 cm line becomes 25 cm?

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If two polygons are similar and one side is 8 and corresponding side is 12, what is the scale factor?

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When scale factor is less than 1, the figure is:

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If perimeter scales by factor k, how does area scale?

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Two similar triangles have areas 9 and 36. What is the scale factor?

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