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