GeometryTriangle inequality
Name: Date:
Can these three lengths form a triangle? Answer Yes or No.
1 YesNo
2 YesNo
3 YesNo
4 YesNo
5 YesNo
6 YesNo
7 YesNo
8 YesNo
Triangle inequality worksheets
Not every three lengths make a triangle. The two shorter sides have to add to more than the longest, or the short pair never reaches across. These free printable worksheets give three lengths and ask, simply, whether they can be the sides of a triangle.
Kid stuck on one? You don’t just get the sheet.
Triangle inequality
The answer key prints on a separate page.
What's on this sheet
The test is one addition and one comparison: add the two shorter lengths and check whether the total beats the longest. If it does, the sides close into a triangle; if it only ties, they lie flat in a line; if it falls short, they never meet. That is the whole triangle inequality, and it is worth stating as reaching rather than as a rule to memorise.
Why this sheet works
The lengths are drawn as three separate sticks, never assembled — laying the short two end to end over the long one would answer the question before a child has thought about it. The comparison stays arithmetic, which is where the standard wants it: given the numbers, could a triangle be built at all?
How this one works
One question from this sheet, worked through a step at a time.
Can it be a triangle?
3+13vs14
16>14
Yes
- Three lengths make a triangle only when the two shorter sides add to more than the longest. The two shorter are 3 and 13; the longest is 14.
- 3 + 13 = 16, which is more than 14.
- The two shorter sides reach past the longest, so they close into a triangle. Yes.