Name the angles opposite of each side:
X is opposite of YZY is opposite of XZZ is opposite of XY
X
Y
Z
Triangle Inequalities
GeometryMrs. 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.
• XY + YZ > XZ• YZ + XZ > XY• XZ + XY > YZ
X
Y
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.
• Ex. If XZ > XY,then mY > mZ
X
Y
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 mY > mZ,then XZ > XY
X
Y
Z
In TUV, Name the sides from shortest to longest
• TV, UV, UT
6258U V
T
Homework
Work Packet:Triangle Inequalities
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