The Triangle Inequality

1
The Triangle Inequality

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

2
Example 4-1c
Determine whether the given measures can be
lengths of the sides of a triangle. a. 6, 9,
16 b. 14, 16, 27
Answer no
Answer yes
3
Example 4-2b
A 4 B 9 C 12 D 16
Answer D
4
The Triangle Inequality

• 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.

5
Example 4-3b