The Triangle Inequality Thm.
&
Inequalities Involving 2 Triangles
Section 5-4 and 5-5
Triangle Inequality Thm.
The sum of the lengths of any two
sides of a triangle is greater than
rd
the length of the 3 side.
B
6
A
AB + BC > AC
7
10
C
Theorem 5-12
The perpendicular segment from a
point to a line is the shortest
segment from the point to the
Y
line.
A
X
.
B
Corollary 5-1
The perpendicular segment from a
point to a plane is the shortest
segment from the point to the
plane.
.
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
rd
3 side of the first triangle is longer
rd
nd
than the 3 side in the 2 triangle.
B
DF > AC
90
C
A
E
100
D
F
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.
B
A
C
10
E
D
F
12
Angle E > Angle B
Joke Time
What would you say if someone
took your playing cards?
dec-a-gon
What kind of insect is good at
math?
an account-ant