Check Similarity in Right Triangles Calculator
Determine if two right triangles are similar and find their scale factor
Check Right Triangle Similarity
First Triangle (enter any 2 sides)
Enter any 2 sides. The third side will be calculated automatically using the Pythagorean theorem.
Second Triangle
The hypotenuse will be calculated automatically from the two legs.
Similarity Analysis
Enter valid triangle measurements to check similarity
Triangle 1: Enter at least 2 sides
Triangle 2: Invalid right triangle
Example: 3-4-5 and 6-8-10 Triangles
Given Triangles:
Triangle 1: sides 3, 4, 5
Triangle 2: sides 6, 8, 10
Similarity Check:
Ratio 1: 6/3 = 2
Ratio 2: 8/4 = 2
Ratio 3: 10/5 = 2
Result: All ratios equal 2, so triangles are similar with scale factor 2
Triangle Similarity Criteria
Angle-Angle
Two corresponding angles equal
Side-Angle-Side
Two sides proportional, included angle equal
Side-Side-Side
All corresponding sides proportional
Right Triangle Facts
Right triangles have one 90° angle
Follow Pythagorean theorem: a² + b² = c²
Similar triangles have equal corresponding angles
Proportional sides indicate similarity
Scale factor = ratio of corresponding sides
Understanding Triangle Similarity
What Makes Triangles Similar?
Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. For right triangles, since one angle is always 90°, we only need to check if the other angles are equal or if the sides are proportional.
Similarity in Right Triangles
- •If corresponding sides are proportional, triangles are similar
- •The proportionality constant is called the scale factor
- •Similar triangles have identical angle measures
- •Reflections may also create similar triangles
How to Check Similarity
Step-by-Step Process:
- 1. Ensure both triangles are valid right triangles
- 2. Order the sides from smallest to largest
- 3. Calculate ratios of corresponding sides
- 4. Check if all ratios are equal
- 5. If equal, triangles are similar
Pythagorean Theorem
a² + b² = c²
Where a and b are legs, c is the hypotenuse
Applications of Similar Triangles
Architecture
Scaling blueprints, maintaining proportions in building design
Engineering
Structural analysis, scaling models, stress calculations
Surveying
Measuring distances, height calculations, triangulation