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6 4 Inequalities in One Triangle

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6 4 Inequalities in One Triangle

  1. 1. 6-4 Inequalities in One Triangle
  2. 2.  If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side. Answers: smallest is Z; largest is Y
  3. 3.   If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle. Name the longest side and the shortest side.
  4. 4.  Corollary 1 ◦ The perpendicular segment from a point to a line is the shortest segment from the point to the line.  Corollary 2 ◦ The perpendicular segment from a point to a plane is the shortest segment from the point to the plane.
  5. 5.    The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Is it possible for a triangle to have sides with lengths 9, 6, and 2? Two sides of a triangle have lengths 8 and 12. The length of the third side can be any number between _____ and _____. Answers: no; 4 and 20

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