2. Ch4.6_TriangleInequalities.notebook October 31, 2011
Postulate
The shortest distance between
2 points is a straight line
A B
C
Is it longer to go from A to B,
or from A to C then C to B?
Triangle Inequality Theorem
The sum of the lengths of any 2 sides
of a triangle MUST BE GREATER than
the length of the 3rd side.
C
AC + CB > AB
CB + AB > AC
AB + AC > CB
A B
If the sum of 2 sides is less than
the 3rd side, a triangle can NOT
be drawn.
Example: Can a triangle have side
lengths 2, 3, 8?
3 + 2 ≯ 8
3
2
8
3. Ch4.6_TriangleInequalities.notebook October 31, 2011
Can a triangle have these side lengths?
2, 2, 3
3, 4, 5
2, 7, 4
1.5, 2.5, 4
Give the range of X
X ____ < X
(18 10)
10
18 X < _____
(18 + 10)
8 < X < 28
X
7.5 _____ < X < _____
5
4. Ch4.6_TriangleInequalities.notebook October 31, 2011
Recap:
If 2 angles are , then the
sides across from them are
Unequal Sides/Angles Thm.
Biggest side is across from biggest angle
Smallest angle is across from smallest side
C List the angles from
smallest to biggest
4
3
A B
2
