Triangle Inequalities

1
Triangle Inequalities

• Can you form a triangle from any three segments?
• Try using lengths of 2, 4, and 5 inches
• Try using lengths of 2, 3, and 6 inches
• Try using lengths of 2, 4, and 6 inches
• What must be true of the lengths of three
  segments in order to use them to construct a
  triangle?
• C-21 Triangle Inequality Conjecture
• The sum of the lengths of any two sides of a
  triangle is greater than the length of the third
  side.

2
Triangle Inequalities

• Investigation
• Where are the Smallest and Largest Angles ?
• Step 1
• Draw a scalene triangle
• Step 2
• Measure all three angles. Label the smallest
  angle S, the middle angle M, and the largest
  angle L.
• Step 3
• Measure the three sides. Label the longest side
  l, the second longest side m, and the shortest
  side s
• Step 4
• Which side is opposite L? M? S?

3
Triangle Inequalities

• C-22  Side-Angle Inequality Conjecture
• In a triangle, if one side is longer than
  another side, then the angle opposite the longer
  side is larger than the angle opposite the
  shorter side.
• An exterior angle of a triangle is the angle
  formed by extending one side past the vertex.
• The adjacent interior angle is next to the
  exterior angle.
• The remote interior angles are the remaining two
  angles.
• How does the sum of angles a and c compare to
  angle b or x?
• C-23  Triangle Exterior Angle Conjecture
• The measure of an exterior angle of a triangle
  is equal to the sum of the remote interior angles.

4
Chapter 3 Retest

• Make arrangements to take the retest on your own
  time
• During a study or after school
• Must be completed by 330 p.m. Monday
• 8 vocabulary questions totaling 8 points
• 5 construction questions totaling 32 points
• Scores on the original and retest will be
  combined to calculate your total score out of 100
• Example 1 25 on original 35 on retest 60
• Grade increases from failing (41.7) to a D-
• Example 2 25 on original 15 on retest 40
• Grade decreases slightly from 41.7 to 40
• Only take the retest if youre sure youll do
  well!