5-4 Triangle Inequality Theorem Theorem 5.11: The sum of the measures of any two sides of a triangle is greater than the measure of the third side. a + b > c b + c > a a + c > b Example 1 – Determine if the three numbers can be the measures of the sides of a triangle. 6, 7, 9 1, 7, 8 yes no: 1 + 7 = 8 it’s not > 8 a b c

Your Turn Try Check your progress 1A & 1B on page 296. 1A: no; 6 + 8 not > 14 1B: yes; 8 + 15 > 17

Example If the measures of two sides of a triangle are 12 meters and 14 meters, find the range of the possible measures of the third side. x > 14 – 12 x > 2 14 + 12 > x 26 > x 2 < x < 26 Try Check Your Progress #2…but find the range (not just the least)

Theorem 5.12 The perpendicular segment from a point to a line is the shortest segment from the point to the line.

Corollary 5.1 The perpendicular segment from a point to a plane is the shortest segment from the point to the plane. Try page 299 #4-8

Homework #34 P. 299 7-12, 13-19 odd, 22-25, 33, 36-37