1. The Triangle Inequality

2. Theorem 5.11
Triangle Inequality Theorem. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. B
Example:
AB + BC > AC
BC + AC > AB
AB + AC > BC C A

3. Determine whether the given measures can be the sides of a triangle.
NO! 6 ½ + 6 ½ > 14 ½
13 > 14 ½ is false.
> 7.5
14 > 7.5
B) 6.8, 7.2, 7.5
> 7.2
14.3 > 7.2
YES!
> 6.8
14.7 > 6.8
Hint: Take the two smallest numbers and add them together. They have to be
larger than the third number or the side lengths cannot form a triangle.

4. Practice Can these numbers form the sides of a triangle? 3, 7, 9
3 + 7 = 10 , 10 > 9, YES!
2, 3, 6
2 + 3 = 5, 5 IS NOT GREATER THAN 6, NO!
10, 10, 19
= 20, 20 > 19, YES!

5. Given the measures of two sides determine the range of the third
Given:  ABC with AB = 7 and BC = 12, determine the
range of AC.
Solve AB + BC > AC
BC + AC > AB
AB + AC > BC B
AB + BC > AC
> AC
19 > AC
BC + AC > AB
12 + AC > 7
AC > -5
AB + AC > BC
7 + AC > 12
AC > 5 A C
Thus AC is less than 19 and greater than 5!
Hint: Add the two numbers together and then subtract
the two numbers! Those are your range values!