Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of...

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Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z

description

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

Transcript of Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of...

Page 1: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.

Name the angles opposite of each side:

X is opposite of YZY is opposite of XZZ is opposite of XY

X

Y

Z

Page 2: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.

Triangle Inequalities

GeometryMrs. King

Unit 4, Day 5

Page 3: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.

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

Page 4: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.

Using the Triangle Inequality Theorem…

• Is it possible for 3, 7, and 8 to be the sides of a triangle?

Page 5: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY X Y Z.

Using the Triangle Inequality Theorem…

• What about 3, 6, and 10?

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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

Page 7: Name the angles opposite of each side: X is opposite of YZ Y is opposite of XZ Z is opposite of XY 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

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In TUV, Name the sides from shortest to longest

• TV, UV, UT

6258U V

T

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Homework

Work Packet:Triangle Inequalities


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