1. 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: = 8 it’s not > 8 a b c

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

3. 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
> x
26 > x
2 < x < 26
Try Check Your Progress #2…but find the range (not just the least)

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

5. 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

6. Homework #34
P , odd, 22-25, 33, 36-37