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Name the angles opposite of
each side:
Y
X
• X is opposite of YZ
• Y is opposite of XZ
• Z is opposite of XY
Z
Triangle Inequalities
Geometry
Mrs. King
Unit 4, Day 5
Triangle Inequality Theorem
• The sum of the length of any two sides of a
triangle is greater than the third side.
Y
• XY + YZ > XZ
• YZ + XZ > XY
• XZ + XY > YZ
X
Z
Using the Triangle Inequality
Theorem…
• Is it possible for 3, 7, and 8 to be the sides
of a triangle?
Using the Triangle Inequality
Theorem…
• What about 3, 6, and 10?
Inequalities Relating Sides and
Angles
• Theorem 4-10: If two sides of a triangle are
not congruent, then the larger angle lies
opposite the longer side.
Y
• Ex. If XZ > XY,
then mY > mZ
X
Z
Inequalities Relating Sides and
Angles
• Theorem 4-11: If two angles of a triangle
are not congruent, then the longer side lies
opposite the larger angle.
• Ex. If mY > mZ,
then XZ > XY
X
Y
Z
In TUV, Name the sides from
shortest to longest
T
58
U
• TV, UV, UT
62
V
Homework
Work Packet:
Triangle Inequalities