1. Inequalities for One Triangle
Section 6-4
Inequalities for
One Triangle

2. Theorem 6-2
If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

3. Example: N D A 6 8 10

4. Theorem 6-3
If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.

5. Example: C A T
CT < TA < CA

6. Corollary 1
The perpendicular segment from a point to a line is the shortest segment from the point to the line.

7. Corollary 2
The perpendicular segment from a point to a plane is the shortest segment from the point to the plane.

8. Theorem 6-4: The Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

9. Example #1:
Is it possible for a triangle to have sides with the lengths as indicated?
a.) 6, 6, 5
b.) 3, 4, 8
c.) 2.5, 4.1, 5.0
Yes No
Yes

10. Example #2:
The lengths of two sides of a triangle are 8 and 13. Then, the length of the third side must be greater than ______ but less than ______. 5 21