1. Lesson 5.4 The Triangle Inequality

2. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side

3. Triangle Inequality Theorem Problems Determine if the measures given could be the sides of a triangle.  16, 17, 19 16 + 17 = 33 yes, the sum of the two smallest sides is larger than the third side  6, 9, 15 6 + 9 = 15 no, the sum of the two smallest sides is equal to the other side so it cannot be a triangle Find the range for the measure of the third side given the measures of two sides.  7.5 and 12.1 12.1- 7.5 < x < 12.1 + 7.5 4.6 < x < 19.6  9 and 41 41-9 < x < 41 + 9 32 < x < 50

4. Determine whether it is possible to form a triangle with side lengths 5, 7, and 8.

5. Find the range for the measure of the third side of a triangle if two sides measure 4 and 13.

6. In ΔPQR, PQ = 7.2 and QR = 5.2. Which measure cannot be PR? A 7 B 9 C 11 D 13