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Inequalities Within a Triangle

Vocabulary. Inequalities Within a Triangle. What You'll Learn. You will learn to identify the relationships between the _____ and _____ of a triangle. sides. angles. Nothing New!. P. 11. 8. M. 13. L. Inequalities Within a Triangle. in the same order. PM <. ML. LP <. m M <.

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Inequalities Within a Triangle

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  1. Vocabulary Inequalities Within a Triangle What You'll Learn You will learn to identify the relationships between the _____ and _____ of a triangle. sides angles Nothing New!

  2. P 11 8 M 13 L Inequalities Within a Triangle in the same order PM < ML LP < mM < mL < mP

  3. K W 45° 75° 60° J Inequalities Within a Triangle in the same order mW < mJ < mK KW < WJ JK <

  4. W X Y Inequalities Within a Triangle greatest measure 5 3 4 WY > XW WY > XY

  5. Inequalities Within a Triangle The longest side is The largest angle is So, the largest angle is So, the longest side is

  6. B A C Triangle Inequality – examples… For the triangle, list the angles in order from least to greatest measure. 4 cm 6 cm 5 cm

  7. Vocabulary Triangle Inequality Theorem What You'll Learn You will learn to identify and use the Triangle Inequality Theorem. Nothing New!

  8. b a c Triangle Inequality Theorem greater a + b > c a + c > b b + c > a

  9. However, 10 + 5 > 16 Triangle Inequality Theorem Can 16, 10, and 5 be the measures of the sides of a triangle? 16 + 10 > 5 No! 16 + 5 > 10

  10. Can 11, 21, and 31 make a Triangle

  11. If two sides of a triangle are 7 & 13, between what two numbers must the third side be? -if 13 is the largest side then the smallest side had to be > 6 (13 < 7 + ? ) -If 7 & 13 are the 2 smaller sides, the 3rd side has to be < 20 (? < 13 + 7 ) Answer: the 3rd side is between 6 and 20. Example: Triangle Inequality

  12. Example Four:Finding Possible Side Lengths • A triangle has sides of lengths 8 and 10. Describe the lengths of the third side. • Let x represent the third side.

  13. Checkpoint

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