Similar Right Triangles Calculator
Calculate missing sides, angles, and properties of similar right triangles using scale factors and proportional relationships
Calculate Similar Right Triangles
First Triangle (△1)
Enter at least 2 sides. The third side will be calculated automatically.
Scale Factor
Ratio of corresponding sides (second triangle ÷ first triangle)
Example Calculation
Given Information
Triangle 1: legs = 3 and 4 units
Scale Factor: 2.5
Find: All measurements of Triangle 2
Solution
Step 1: Complete Triangle 1: c = √(3² + 4²) = √25 = 5
Step 2: Scale Triangle 1 by factor 2.5:
• Triangle 2 legs: 3 × 2.5 = 7.5 and 4 × 2.5 = 10
• Triangle 2 hypotenuse: 5 × 2.5 = 12.5
Step 3: Areas: Triangle 1 = 6, Triangle 2 = 37.5
Result: Triangle 2 has sides 7.5, 10, and 12.5 units
Triangle Similarity Properties
Same Angles
All corresponding angles are equal
Proportional Sides
Corresponding sides are in proportion
Scale Factor
Ratio of corresponding sides
Right Triangle Facts
One angle is exactly 90°
Follows Pythagorean theorem: a² + b² = c²
Area = (leg₁ × leg₂) ÷ 2
Similar triangles have same angle measures
Calculator Tips
Enter at least 2 sides of the first triangle
Use scale factor if you know the size ratio
Enter known sides of second triangle to find scale factor
Areas scale by the square of the scale factor
Understanding Similar Right Triangles
What are Similar Right Triangles?
Two right triangles are similar if they have the same three angles and their corresponding sides are proportional. Since both triangles have a 90° angle, they only need one more pair of equal angles to be similar.
Properties of Similar Triangles
- •All corresponding angles are equal
- •Corresponding sides are proportional
- •The ratio of areas equals the square of the scale factor
- •The ratio of perimeters equals the scale factor
Scale Factor
Scale Factor = Side₂ / Side₁
The scale factor is the ratio of any corresponding sides between two similar triangles. It tells us how many times larger (or smaller) the second triangle is compared to the first.
Key Formulas
- Pythagorean Theorem: a² + b² = c²
- Area: A = (leg₁ × leg₂) / 2
- Area Ratio: A₂/A₁ = (scale factor)²
- Perimeter Ratio: P₂/P₁ = scale factor