Triangle Similarity Checker
Enter the known sides and angles of two triangles. The Triangle Similarity Checker will instantly determine if they are similar and which theorem applies.
Triangle A
Triangle B
About the Triangle Similarity Checker
The Triangle Similarity Checker is a scientifically accurate tool that instantly determines whether two triangles are similar using the four accepted similarity criteria: AA, SSS, SAS, and SAS (proportional sides with included angle). This Triangle Similarity Checker implements rigorous Euclidean geometry theorems as presented in standard textbooks (Moise 1990; Hartshorne 2000) and is trusted by students, teachers, and mathematicians worldwide. Proudly supported by Agri Care Hub.
The Four Triangle Similarity Theorems
SSS (Side-Side-Side) – All three side ratios equal
SAS (Side-Angle-Side) – Two sides proportional and included angle equal
ASA (Angle-Side-Angle) – Two angles and included side proportional
Why the Triangle Similarity Checker Is Important
Triangle similarity is one of the most powerful concepts in geometry. When two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional. This principle underpins trigonometry, map-making, computer graphics, architecture, engineering, optics, and astronomy. Understanding similarity allows us to solve real-world problems involving indirect measurement (e.g., finding the height of a building using shadows) and scale models.
How to Use the Triangle Similarity Checker
- Enter all known sides and angles for both triangles.
- Leave unknown values blank.
- You need at least two angles or three pieces of information per triangle.
- Click “Check Triangle Similarity”.
- The tool instantly reports if the triangles are similar and which theorem proves it.
When Should You Use This Calculator?
- High-school geometry homework and exams
- Preparing for SAT, ACT, GCSE, IB, or university entrance tests
- Teaching similarity theorems in the classroom
- Architecture, surveying, and engineering scale problems
- Computer graphics and 3D modeling verification
- Any situation requiring indirect measurement using similar triangles
Scientific Foundation
All similarity theorems are rigorously proven in Euclidean geometry. AA is taken as a postulate in most modern treatments. SSS and SAS similarity follow from the basic proportionality theorem (Thales’ theorem) and the properties of parallel lines. The proofs are standard and appear in every reputable geometry textbook. Full mathematical treatment available at Triangle Similarity on Wikipedia.
Limitations
The checker works for plane Euclidean triangles only. It correctly identifies SSA as NOT a similarity criterion (SSA is the ambiguous case and does not guarantee similarity). Very small numerical differences (less than 0.01) are treated as equal to account for rounding.
Conclusion
The Triangle Similarity Checker brings centuries of geometric knowledge into an instant, user-friendly tool. Whether you’re a student mastering similarity, a teacher demonstrating theorems, or a professional working with scale and proportion, this checker delivers mathematically perfect results every time. For more educational tools, visit Agri Care Hub.