Similar Triangles Calculator

Author: Henrick Yau
- 12 December 2025
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Similar Triangles Calculator

Calculate and verify similarity between triangles using different criteria such as Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Angle (AA), and find unknown side lengths and angles.

Similarity Criteria Selection

Use the properties of similar triangles to find an unknown side length.

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Display Options

About Similar Triangles

Similar triangles have the same shape but not necessarily the same size. Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional.

Similarity Criteria
  • Angle-Angle (AA): Two triangles are similar if two angles of one triangle are equal to two angles of another triangle. (The third angle will also be equal.)
  • Side-Side-Side (SSS): Two triangles are similar if all their corresponding sides are proportional.
  • Side-Angle-Side (SAS): Two triangles are similar if two sides of one triangle are proportional to two sides of another triangle, and the included angles are equal.
Properties of Similar Triangles
  • Corresponding angles are equal.
  • Corresponding sides are proportional.
  • The ratio of corresponding sides is called the scale factor (or similarity ratio).
  • The ratio of the areas of similar triangles is equal to the square of the scale factor.
  • The ratio of the perimeters of similar triangles is equal to the scale factor.
Applications of Similar Triangles

Similar triangles have numerous practical applications, including:

  • Finding heights of tall objects indirectly
  • Solving real-world proportionality problems
  • Map scaling and distance calculations
  • Architecture and engineering design
  • Optical systems and lens calculations