The Triangle Inequality Thm.

1
The Triangle Inequality Thm.Inequalities
Involving 2 Triangles

• Section 5-4 and 5-5

2
Triangle Inequality Thm.

• The sum of the lengths of any two sides of a
  triangle is greater than the length of the 3rd
  side.

B
AB BC gt AC
6
7
C
A
10
3
Theorem 5-12

• The perpendicular segment from a point to a
  line is the shortest segment from the point to
  the line.

Y
A
.
X
B
4
Corollary 5-1

• The perpendicular segment from a point to a
  plane is the shortest segment from the point to
  the plane.

.
5
SAS Inequality (Hinge Thm.)

• If 2 sides of one triangle are congruent to 2
  sides of another triangle, and the included angle
  in one triangle is greater than the included
  angle in the other, then the 3rd side of the
  first triangle is longer than the 3rd side in the
  2nd triangle.

6
B
DF gt AC
90
C
A
E
100
F
D
7
SSS Inequality

• If 2 sides of one triangle are congruent to 2
  sides of another triangle and the 3rd side in one
  triangle is longer than the third side in the
  other, then the angle between the pair of
  congruent sides in the first triangle is greater
  than the corresponding angle in the 2nd triangle.

8
B
C
A
10
E
D
F
12
Angle E gt Angle B
9
Joke Time

• What would you say if someone took your playing
  cards?
• dec-a-gon

10

• What kind of insect is good at math?
• an account-ant