Triangle Inequality Theorem

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Triangle Inequality Theorem
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Triangle Inequality Theorem

• The sum of the two shorter sides of any triangle
  must be greater than the third side.

Example 3 5 gt 7 8 gt 7
Yes!
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Practice

• Decide if it is possible to construct a triangle
  having the given side lengths. If not, explain.

13mm, 25mm, 14mm 13 14 gt 25 27 gt 25 Yes!
9in, 17in, 8in 8 9 gt 17 17 gt 17 No!
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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.

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Practice

• m?____ lt m?____ lt m?____
• _______ lt ______ lt _______

m?____ lt m?____ lt m?____ _______ lt ______
lt _______
C
B
A
X
Z
Y
___ AC
___ BC
___ BA
___ XZ
___ YZ
___ XZ
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Practice

• List the sides in order from least to greatest

List the angles in order from least to
greatest
___ UT ,
___ ST ,
___ SU
ltH, ltJ, ltI
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Practice