1. 5.4 The Triangle Inequality What you’ll learn: 1.To apply the triangle inequality Theorem 2.To determine the shortest distance between a point and a line.

2. Theorems Theorem 5.11 Triangle Inequality Theorem The sum of the lengths of any 2 sides of a triangle is greater than the length of the 3 rd side. Theorem 5.12 The perpendicular segment from a point to a line is the shortest segment from the point to the line.

3. Determine whether the given measures can be the lengths of the sides of a triangle 1.6½, 6½, 14½ no, 6½+6½ is not greater than 14½ 2.6.8, 7.2, 5.1 yes, 5.1+6.8=7.2 3.6, 7, 13 no 6+7 is not greater than 13

4. Finding the range of possible 3 rd side lengths 1.5, 8 8-5=3 and 5+8=13 3<x<13 2.7, 10 10-7=3 and 10+7=17 3<x<17 3.9, 9 9-9=0, 9+9=18 0<x<18

5. Homework p. 264 14-38 even, 42, 44, 56