What if you had to determine whether the three lengths 5, 7, and 10 make a triangle?
Triangle Inequality Theorem
The arc marks show that the two sides would never meet to form a triangle. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third.
Determining if Three Lengths make a Triangle
Do the lengths 4, 11, 8 make a triangle?
Solving for an Unknown Length
Find the length of the third side of a triangle if the other two sides are 10 and 6.
Making Conclusions about the Length of Legs
The base of an isosceles triangle has length 24. What can you say about the length of each leg?
Each leg must have a length greater than 12.
Earlier Problem Revisited
The three lengths 5, 7, and 10 do make a triangle. The sum of the lengths of any two sides is greater than the length of the third.
Do the lengths below make a triangle?
Use the Triangle Inequality Theorem. Test to see if the smaller two numbers add up to be greater than the largest number.
4.1, 3.5, 7.5
4, 4, 8
6, 7, 8
Determine if the sets of lengths below can make a triangle. If not, state why.
- 6, 6, 13
- 1, 2, 3
- 7, 8, 10
- 5, 4, 3
- 23, 56, 85
- 30, 40, 50
- 7, 8, 14
- 7, 8, 15
- 7, 8, 14.99
If two lengths of the sides of a triangle are given, determine the range of the length of the third side.
- 8 and 9
- 4 and 15
- 20 and 32
- 2 and 5
- 10 and 8
- The legs of an isosceles triangle have a length of 12 each. What can you say about the length of the base?
To view the Review answers, open this PDF file and look for section 5.7.