How this calculator works
Similar triangles have equal corresponding angles and proportional corresponding sides. SSS checks all three side ratios. SAS requires proportional pairs and their equal included angle; comparing the resulting complete triangles performs that check. AA compares two corresponding angle pairs. Scaling mode uses one positive factor for every side. The missing-side mode assumes similarity has already been established. Numerical equality uses a relative tolerance of 1 in 10 billion.
Formula
k=d/a=e/b=f/c; P₂=kP₁; K₂=k²K₁; missing e=b(d/a). AA requires A=D and B=E.
Worked example
A 3-4-5 triangle scaled by 2 becomes 6-8-10. Its perimeter grows from 12 to 24 and its area grows from 6 to 24. If 3 corresponds to 6, a side of 4 corresponds to 8.
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Frequently asked questions
Does one matching ratio prove similarity?
No. One ratio sets a candidate scale, but other corresponding sides or angles must confirm the shape.
Can I enter the sides in any order?
Use matching order in both triangles. Reordering only one triangle changes the correspondence being tested.
Can angles determine the scale factor?
No. AA determines shape only, so the calculator does not report scale, area or perimeter without a length measurement.