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Triangle Inequality Theorem
Triangle Inequality Theorem
 The sum of the two shorter sides of any triangle must be greater than the
third side.
Example:
3+5>7
8 >7
Yes!
Practice
Decide if it is possible to construct a
triangle having the given side lengths.
If not, explain.
13mm, 25mm, 14mm
9in, 17in, 8in
13 + 14 > 25
27 > 25
Yes!
8 + 9 > 17
17 > 17
No!
Sides & Angles
 The longest side of a triangle is
always across from the largest
angle. The shortest sides of a
triangle is always across from the
smallest angle.
Practice
A < m____
C < m____
B
m____
___
___
___
AC
_______
< ______
BC
BA < _______
Z < m____
X < m____
Y
m____
___
___
___
XZ
YZ < _______
_______
< ______
XZ
Practice
List the sides in order from
least to greatest:
___
___ ___
UT ,
ST ,
SU
List the angles in order
from least to greatest:
<H, <J, <I
Practice