Inequalities in One Triangle

1
Section 5-5

• Inequalities in One Triangle

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Theorem 5-10

• Longest side?Largest angle
• Shortest side? Smallest angle

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Example
4
Theorem 5-11(Converse)

• Largest angle?Longest side
• Smallest angle?Shortest side

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Example
6
Shortest Side _________ Shortest Side
_________ Shortest Side _________ Largest
Side _________ Largest Side _________ Largest
Side _________
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Smallest Angle _________ Smallest Angle
_________ Smallest Angle _________ Largest
Angle _________ Largest Angle _________ Largest
Angle _________
8
(No Transcript)
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List the sides from least to greatest
O
55
50
75
P
55
87
38
N
M
10
RECALLExterior Angle Theorem
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Exterior Angle Inequality Theorem

• The measure of an exterior Angle is always
  greater than the measure of a non-adjacent angle

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(No Transcript)
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Triangle Inequality Theorem

• The sum of the lengths of any two sides of a
  triangle is greater than the length of the third
  side.
• Side Side gt Largest Side

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Example 1

• Is it possible for a triangle to have sides with
  the lengths as indicated?
• a.) 6, 6, 5
• b.) 3, 4, 8
• c.) 2.5, 4.1, 5.0

Yes
No
Yes
15
Practice Problems

1. 5in, 2in, 8in.
2. 6m, 12m, 15m
3. 3ft, 2ft, 3 ft
4. 50cm, 60cm, 111cm
5. 1in, 1in, 2in

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The lengths of two sides of a triangle are 8 and
10. Then, the length of the third side must be
greater than ______ but less than ______.
2
18
2ltxlt18
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Practice Problems

• Find possible measures for the 3rd segment of the
  triangle given side lengths
• 7 and 12
• 7 and 8
• 9 and 15
• 12 and 13
• 5 and 5

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More practice problems!!

• Solve the inequality ABACgtBC

A
x 2 x 3 gt 3x 2 2x 5 gt 3x 2
7 gt x x lt 7
x 2
x 3
C
B
3x - 2