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5.5 Inequalities in Triangles

5.5 Inequalities in Triangles. Can you figure out the puzzle below???. DOM. Domino. Comparison Property of Inequality. a. b. c. Comparison Property of Inequality: If a = b + c , and c > 0, then a > b. Theorem.

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5.5 Inequalities in Triangles

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  1. 5.5 Inequalities in Triangles Can you figure out the puzzle below??? DOM Domino

  2. Comparison Property of Inequality a b c Comparison Property of Inequality: If a = b + c, and c > 0, then a > b.

  3. Theorem Corollary to the Triangle Exterior Angle Theorem: The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles. 3 1 2

  4. Application Given the figure below, explain why . Statements Reasons 1. 2. 3. 1. 2. 3.

  5. Theorem Theorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

  6. Example List the angles of the following figure in order from smallest to largest.

  7. Theorem Theorem 5-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.

  8. Sides of a Triangle List the sides of the following triangle in order from shortest to longest. Determine which segment is shortest in the following diagram.

  9. Theorem Theorem 5-12: Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

  10. Theorem Can a triangle have sides with the given lengths? a) 7 ft, 3 ft, 8 ft b) 10 cm, 6 cm, 3 cm A triangle has sides of lengths 8 cm and 10 cm. Describe the lengths possible for the third side.

  11. 5.5 Inequalities in Triangles Can you figure out the puzzle below??? HW 5.5: #1-25 (1st column), 32, 33, 35 p.192: #3-4, 11, 22, 24-26 ESGG SGEG GEGS SGGE Scrambled Eggs

  12. Proof of Comparison Property of Inequality Given: a = b + c, c > 0 Prove: a > b Statements Reasons c > 0 b + c > b + 0 b + c > b 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. a = b + c a > b

  13. Midterm Review Given the figure below, name the type of angle pairs given.

  14. Midterm Review Find . Justify each answer. 1) 2) 1 135° 2

  15. Midterm Review Find x in the following polygon. x° 125° 125°

  16. Midterm Review Find the equation of a line that goes through the point (-2, 1) and (3,2). Find the equation of a line parallel to y + 3x = 5 that goes through the point (-3, 5).

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