Triangle Inequality Checker
Triangles · Class IX
Pick three side lengths a, b, c. Do they form a valid triangle?
- a + b > c?1
- b + c > a?1
- a + c > b?1
- Valid triangle?1
Formulas in this lab
- a + b > c?
- b + c > a?
- a + c > b?
- Valid triangle?
Frequently asked questions
▶What is the triangle inequality?
For any triangle with sides a, b, c, the sum of any two sides must exceed the third: $a + b > c$, $b + c > a$, and $c + a > b$. If even one inequality fails, the three lengths cannot close into a triangle.
▶How do I use this lab?
Slide the three sides a, b, c between 0.5 and 20. The lab checks all three inequalities and tells you whether a valid triangle is formed. Try 3, 4, 5 (works) versus 1, 2, 5 (fails).
▶Common mistake on this topic
Students check only one inequality and stop. You must verify all three pairs before concluding a triangle is possible. In board exams, write each inequality clearly to score full marks.
▶Where do we use this idea?
Carpenters cutting bamboo poles for a frame check the triangle rule before joining sides. If a tailor cuts three strips for a triangular flag, the longest must be less than the sum of the other two, else the flag won't close.