Similar Triangles Comparison

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About This MicroSim

This interactive visualization demonstrates the relationship between two similar triangles. Use the slider to adjust the scale factor and observe how:

• Corresponding sides maintain proportional relationships
• Corresponding angles remain equal (shown with matching color markers)
• The area scales by the square of the scale factor (k²)

Key Concepts

Similar Triangles have: - All corresponding angles congruent (equal) - All corresponding sides proportional (same ratio)

Scale Factor (k): - k > 1: The second triangle is an enlargement - k < 1: The second triangle is a reduction - k = 1: The triangles are congruent

Mathematical Relationships

For similar triangles △ABC ~ △DEF with scale factor k:

• DE/AB = EF/BC = DF/AC = k (sides are proportional)
• ∠A = ∠D, ∠B = ∠E, ∠C = ∠F (angles are equal)
• Area(△DEF)/Area(△ABC) = k²

Learning Objectives

• Understand the definition of similar figures
• Apply scale factors to find corresponding side lengths
• Recognize the relationship between scale factor and area ratio

Bloom's Taxonomy Level

Understanding and Applying