What you’ll learn
Determine whether triangle conditions are possible.
Key idea
Triangle inequalities are strict; equality makes a straight degenerate figure.
Both difference and sum bounds are strict; equality gives a degenerate segment, and inverse shortening must satisfy all three pairwise inequalities.
Worked example
Enter the exact value or ordered values in the format requested below.
Two triangle sides are 2cm and 5cm. A proposed third side 7cm is too long or at equality. Enter the greatest whole-number third-side length that can form a nondegenerate triangle.
- A nondegenerate triangle requires |2-5|<c<7.
- Greatest whole-number c is 6; proposed side 7 must drop by at least 1 to reach 6.
Answer: 6
Quick Check
Evaluate a worked attempt at determine whether triangle conditions are possible, identify the first invalid step, and provide the correction.
Sides 2,10,12cm are checked after considering proposed length 12cm. Step1: 2+10=12. Step2: equality satisfies triangle inequality, so a triangle exists. Locate the first invalid step and correct the judgment.