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.

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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.

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.

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, = , 7, 13 no 6+7 is not greater than 13

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

Homework p even, 42, 44, 56