Similar Triangles Calculator
Check triangle similarity and find missing sides using scale factors and similarity criteria
Calculate Similar Triangles
Triangle ABC
Triangle DEF
Input Requirements:
• Enter all three sides for both triangles to check SSS similarity
Example Calculation
SSS Similarity Check
Triangle ABC: AB = 4, BC = 6, AC = 8
Triangle DEF: DE = 8, EF = 12, DF = 16
Solution
DE/AB = 8/4 = 2.000
EF/BC = 12/6 = 2.000
DF/AC = 16/8 = 2.000
Result: All ratios equal, triangles are similar (k = 2)
Similarity Criteria
Side-Side-Side
All corresponding sides are proportional
DE/AB = EF/BC = DF/AC = k
Side-Angle-Side
Two sides proportional, included angles equal
DE/AB = DF/AC, ∠A = ∠D
Angle-Side-Angle
Two angles equal, corresponding sides proportional
∠A = ∠D, ∠B = ∠E
Scale Factor Properties
Sides and perimeters scale by factor k
New_length = Original_length × k
Areas scale by factor k²
New_area = Original_area × k²
Angles remain unchanged
Corresponding angles are equal
Similarity Tips
Similar triangles have the same shape but different size
Corresponding angles are always equal in similar triangles
Scale factor k > 1 means enlargement, k < 1 means reduction
All equilateral triangles are similar to each other
Understanding Similar Triangles
What Makes Triangles Similar?
Two triangles are similar if their corresponding sides are proportional and their corresponding angles are equal. This means one triangle is a scaled version of the other.
Similarity Symbol
We use the symbol ~ to indicate similarity. For example, △ABC ~ △DEF means triangle ABC is similar to triangle DEF.
Scale Factor
The scale factor (k) is the ratio of corresponding sides. If k = 2, then triangle DEF is twice as large as triangle ABC in all linear dimensions.
Key Formulas
Similarity Ratio
DE/AB = EF/BC = DF/AC = k
All corresponding sides have the same ratio
Area Relationship
Area₂ = Area₁ × k²
Areas scale by the square of the scale factor
Perimeter Relationship
Perimeter₂ = Perimeter₁ × k
Perimeters scale by the scale factor
Applications
Architecture & Engineering
- • Scale models and blueprints
- • Structural similarity analysis
- • Proportional design scaling
Photography & Art
- • Image resizing and cropping
- • Perspective and proportion
- • Map scaling and cartography