GEOMETRY CHAPTER 6
INEQUALI
TIES IN TRIANGLES
**CHECK ODD ANSWERS IN THE BACK OF THE BOOK**
6.1
Inequalities
Properties of Inequalities
Exterior Angle Inequality Theorem
page 206

7
#1

5, 8
6.4
Inequalities for One Triangle
Theorems involving in
equality for one triangle
page 222

23
#1

12, 15

17
6.5
Inequalities for Two Triangle
Theorems involving inequality for two triangles
SAS and SSS Inequality Theorem
page 231

33
#3

8
CHAPTER 6 TEST
Thm. 6

1: Exterior Angle Ineq
uality Thm.
The measure of an exterior angle of a triangle is greater than the measure of
either remote interior angle.
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 o
pposite the second side.
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.
Corollary 1:
The perpendicular segment from a point to a line is t
he 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.
Theorem 6

4: The Triangle Inequality
The sum of the lengths of any two sides of a triang
le is greater than the third
side.
Thm 6

5: SA
S Inequality Theorem
If two sides of one triangle are congruent to two sides of another triangle, but the
included angle of the first triangle is larger than the included angle of the second
triangle, then the
third side of the first triangle is longer than the third side
of the second triangle.
Thm 6

6: S
SS Inequality Theorem
If two sides of a triangle are congruent to two sides of another triangle, but the
third side of the first triangle is longer than the
third side of the second triangle,
then the included angle of the first triangle is larger than the included angle of
the second triangle.
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