Triangle Similarity Calculator
Check triangle similarity using SSS, SAS, and AA criteria. Find scale factors and missing values
Triangle Similarity Analysis
Triangle ABC
Triangle DEF
Similarity Analysis Results
Side Ratios:
Similarity Criteria Examples
SSS (Side-Side-Side) Similarity
Triangle 1: Sides = 3, 4, 5
Triangle 2: Sides = 6, 8, 10
Ratios: 6/3 = 2, 8/4 = 2, 10/5 = 2
Result: Similar triangles with scale factor 2
SAS (Side-Angle-Side) Similarity
Triangle 1: Sides = 4, 6; Included angle = 60°
Triangle 2: Sides = 8, 12; Included angle = 60°
Ratios: 8/4 = 2, 12/6 = 2; Same angle
Result: Similar triangles with scale factor 2
AA (Angle-Angle) Similarity
Triangle 1: Angles = 30°, 60°, 90°
Triangle 2: Angles = 30°, 60°, 90°
Condition: Two pairs of corresponding angles are equal
Result: Similar triangles (all 30-60-90 triangles are similar)
Similarity Criteria
Side-Side-Side
All corresponding sides are proportional
Side-Angle-Side
Two sides proportional + included angle equal
Angle-Angle
Two pairs of corresponding angles equal
Similar Triangle Properties
Scale Factor
Ratio of corresponding sides
Area Scaling
Area ratio = (scale factor)²
Perimeter Scaling
Perimeter ratio = scale factor
Quick Tips
Corresponding angles in similar triangles are equal
Corresponding sides are proportional by the same ratio
AA criterion is often the easiest to verify
Scale factor > 1 means enlargement
Understanding Triangle Similarity
What Makes Triangles Similar?
Two triangles are similar if they have the same shape but not necessarily the same size. This means all corresponding angles are equal and all corresponding sides are proportional.
Similarity vs. Congruence
- •Similar: Same shape, different size
- •Congruent: Same shape and same size
- •All congruent triangles are similar
Mathematical Notation
SSS Similarity
AB/DE = BC/EF = AC/DF
SAS Similarity
AB/DE = BC/EF and ∠B = ∠E
AA Similarity
∠A = ∠D and ∠B = ∠E
Applications
- • Trigonometry and measurement
- • Scale drawings and maps
- • Photography and optics
- • Engineering and architecture