Similar triangles have the same shape but not necessarily the same size. They let you measure tree heights from shadows, scale maps and models, and they underlie all of trigonometry.
How to use the Similar Triangles Calculator
- Mode
- Criterion
- AB
- BC
- AC
- DE
- EF
- DF
- ∠A (°)
- ∠D (°)
- ∠B (°)
- ∠E (°)
- AB
- BC
- AC
- DE
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
In check mode choose the criterion and enter the matching sides or angles. In find mode enter the three sides of ABC and the side DE of the similar triangle; the scale factor gives the rest.
Formula
SSS: DE/AB = EF/BC = DF/AC · SAS: DE/AB = EF/BC and ∠B = ∠E · AA: ∠A = ∠D and ∠B = ∠E
Area ratio = k²
Worked example
Inputs — Mode: Check similarity; Criterion: SSS (three sides); AB: 3; BC: 4; AC: 5; DE: 6; EF: 8; DF: 10.
Results — Result = The triangles are similar (SSS); Details = DE/AB = 2, EF/BC = 2, DF/AC = 2; Scale factor and area ratio = Scale factor k = 2, area ratio k² = 4.
Key terms
- Scale factor
- The ratio of corresponding sides.
Frequently asked questions
What are similar triangles?
Triangles with equal angles and proportional sides.
Are congruent triangles similar?
Yes, with scale factor 1.
How does area scale?
By the square of the scale factor.
How do shadows measure heights?
The object and a stick form similar triangles with their shadows.