Similar Triangles Calculator
Check similarity using AA, SSS, or SAS and find the scale factor
Triangle 1
Triangle 2
Triangle Similarity Theorems
AA (Angle-Angle)
If two angles of one triangle equal two angles of another, the triangles are similar.
SSS Similarity
If all three pairs of corresponding sides are proportional, the triangles are similar.
SAS Similarity
If two pairs of sides are proportional and included angles are equal, the triangles are similar.
Properties of Similar Triangles
- Corresponding angles are equal
- Corresponding sides are proportional: a₁/a₂ = b₁/b₂ = c₁/c₂ = k
- Perimeter ratio = k
- Area ratio = k²
Finding Missing Sides
Once you know the scale factor k, you can find any missing side:
Frequently Asked Questions
What does similar mean?
Similar triangles have the same shape but possibly different sizes. All angles are equal, and all sides are proportional.
Why is AA enough to prove similarity?
If two angles are equal, the third must be too (since angles sum to 180°). Three equal angles means same shape = similar.
What is the scale factor?
The scale factor k is the ratio of corresponding sides. If k = 2, one triangle is twice as large as the other.
How does area relate to scale factor?
Area scales as k². If one triangle is twice as large (k = 2), its area is 4 times larger (2² = 4).
Are all congruent triangles similar?
Yes! Congruent triangles are similar with scale factor k = 1. Congruence is a special case of similarity.
Are all equilateral triangles similar?
Yes! All equilateral triangles have three 60° angles, so they're all similar to each other by AA.