1. CHAPTER 6: Inequalities in Geometry
Section 6-4:
Inequalities for One Triangle

2. THEOREM 6-2
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. THEOREM 6-3
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.

4. COROLLARIES TO TH. 6-3 Corollary 1
The perpendicular segment from a point to a line is the shortest segment from the point to the line.
Corollary 2
The perpendicular segment from a point to a plane is the shortest segment from the point to the plane.

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

6. PRACTICE Largest angle: I Smallest angle: JH
Name the largest angle and the smallest angle of the triangle. 10 6 I J 8
Largest angle: I
Smallest angle: J

7. Complete With <, =, or >.
Given: ∆ ABC is a right triangle with the measure of angle C = 90.
Conclusions:
> =
<
m∕_C
m ∕_C AC
m ∕_A
m ∕_A + m ∕_B AB

8. PRACTICE
Then, the length of the third side must be greater than ___ but less than ___.
5, 21
7, 27
9, 15
The lengths of two sides of a triangle are:
8 and 13
10 and 17
3 and 12

9. Is it possible for a triangle to have sides with the lengths indicated?
6, 8, 10
3, 4, 8
2.5, 4.1, 5.0
4, 6, 2
6, 6, 5
Yes No

10. Name the largest angle and the smallest angle of the triangle.B
Largest: A
Smallest: C
Largest: R
Smallest: Q 1. 25 29 A C 26 R 2. 12 11 Q 13 S

11. CLASSWORK/HOMEWORK CLASSWORK: PG. 221: CE 1-12
HOMEWORK: WORKSHEET