5-3 Inequalities in One Triangle

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5-3 Inequalities in One Triangle
You found the relationship between the angle
measures of a triangle.

• Recognize and apply properties of inequalities to
  the measures of the angles of a triangle.

• Recognize and apply properties of inequalities to
  the relationships between the angles and sides of
  a triangle.

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Page 344
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• The definition of inequality and the properties
  of inequalities can be applied to the measures of
  angles and segments, since these are real numbers.

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By the Exterior Angle Inequality Theorem, m?14 gt
m?4 and m?14 gt m?11. In addition, m?14 gt m?2 and
m?14 gt m?4 m?3, so m?14 gt m?4 and m?14 gt m?3.
Since ?11 and ?9 are vertical angles, they have
equal measure, so m?14 gt m?9. m?9 gt m?6 and m?9
gt m?7, so m?14 gt m?6 and m?14 gt m?7.
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The Littlest Angle
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C

1. Draw a scalene triangle.
2. Measure the three sides.
3. Measure the three angles.
4. What relationship do you see between the sides
   and the angles?

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Name the largest and smallest angles
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Name the largest and smallest angles
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List the angles of ?ABC in order from smallest
to largest.
Answer ?C, ?A, ?B
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Name the longest and shortest segments
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Name the longest and shortest segments
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List the sides of ?ABC in order from shortest to
longest.
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Theorems

• If two sides of a triangle have unequal lengths,
  then the measure of the angle opposite the longer
  side is greater than the measure of the angle
  opposite the shorter side.
• If two angles of a triangle have unequal
  measures, then the side opposite the large angle
  is longer than the side opposite the smaller angle

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5-3 Assignment

• Page 348, 8-12, 14-19, 22-28 even