How this calculator works
All right triangles share one angle, but similarity also requires a matching acute angle. Equivalently, their corresponding leg ratios must agree. Sorting the legs avoids a false mismatch when labels are reversed. All-sides mode checks both hypotenuses before comparing shape. Ratios are compared with a relative tolerance of 10^-10, intended for numerical roundoff rather than measurement uncertainty.
Formula
c=√(a²+b²); f=√(d²+e²). Similarity requires short₂/short₁ = long₂/long₁ = k. Area scale = k².
Worked example
Legs 3 m, 4 m and 8 m, 6 m form similar right triangles after matching 3 with 6 and 4 with 8. Each length doubles and area increases by four. A 5-12-13 triangle is not similar to a 3-4-5 triangle.
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Frequently asked questions
Are any two right triangles similar?
No. Sharing a right angle is only one matching angle. The ratio of their legs must also match.
Why can the leg labels be swapped?
Similarity concerns shape. The shorter leg corresponds to the shorter leg even if they have different labels in your drawings.
Why is no scale shown for a failed check?
Different side pairs then have different ratios, so there is no single similarity scale. The comparison table still shows each ratio.