Geometry - Triangle Inequalities - Chapt. 6

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Author:
Mamadams
ID:
290485
Filename:
Geometry - Triangle Inequalities - Chapt. 6
Updated:
2014-12-05 21:50:10
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Triangle Inequalites
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Description:
Ch.6 Triangle Inequalities
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  1. Transitive:
    If a < b and b < c then __a < c______
     
  2. Transitive:
    If a > b and b > c then __a > c___
     
  3. Substitution:
    If a > b and b = c then ____a > c____
     
  4. Addition and Subtraction:

    Inequality ___does NOT___ change when adding and subtracting.

    If a > b then a + c > b + c
    Add ≠
  5. Multiplication and Division:

    ** If c > 0

    Inequality __does NOT___ change when multiplying or dividing by positive number

    If a > b then 3a > 3b
    Multiplication ≠
  6. Multiplication and Division:

    ** If c < 0

    Inequality __does____ change when multiplying and dividing by negative number

    If a > b then    <
  7. Whole is always __greater than__ either part!
     
  8. Define:
    Exterior Angle ≠ Theorem
    The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

  9. Exterior < ≠ Theorem
    The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

    < BCD > m < A
    < BCD > m < B
  10.  
    Exterior < ≠ Theorem
    The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

    m < 4  >  m < 1
    m < 4  >  m < 2
  11. If one side of triangle is greater than another side, then the measure of the angle opposite the __big___ side is __greater__ than the measure of the angle opposite the _small__ side.
  12. If the measure of one angle of a triangle is greater than the measure of another angle of the triangle, then the side ____opposite___ the bigger angle is ___bigger___ than the side opposite the smaller angle.


  13. List the angles and sides in order from least to greatest.
    • PQ, QR, RP
    • 17, 21, 26
  14. Define:

    Triangle Inequality Theorem
    The sum of the lengths of any two sides of triangle must be greater than the length of the third side.
  15. The perpendicular segment form a point to a line is the shortest segment from the point to the line

  16. Which side of the triangle above is the smallest?
    In order to find out which side of the triangle is the smallest, we must first sure out which angle of the triangle is the smallest (because the smallest side will be the opposite the smallest angle). We must use the Triangle Angle Sum Theorem to figure out the measure of the missing angle.

    • m < D + m < E + m < V = 180
    • 48 + 87 + m < V = 180
    • 135 + m < V = 180
    • m < V = 45
  17. SAS ≠

    If two sides are congruent to another triangle and the included angle in the first is larger than the opposite triangle's one, then the side is longer than the other side
  18. SSS ≠

    If two sides are congruent to the other triangle, then the angle is greater than the other angle

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