Triangle Inequalities

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Triangle Inequalities
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Information
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Triangle inequality theorem
Triangle inequality theorem The sum of any two
sides of a triangle is greater than the third
side.
AB BC gt AC AB AC gt BC BC AC gt AB
Two sides of a triangle have length AB 4 and AC
8. What can you say about the length of the
third side, BC?
C
By the triangle inequality theorem, the length of
the third side must be strictly less than the sum
of the two other sides
B
BC lt AB AC 4 8 12 BC lt 12
A
4
Finding possible lengths
The length of one side can be any value greater
than the difference and less than the sum of the
other sides
a lt b c
triangle inequality
b lt a c
a different triangle inequality
b c lt a for b gt c
?
b c lt a lt b c
combining inequalities
If b 8 cm and c 6 cm, what is the range of
possible lengths for a?
b
b c lt a lt b c
a
8 6 lt a lt 8 6
substituting
2 lt a lt 14
c
a must measure between 2 cm and 14 cm.