Geometry 5-5 Inequalities in Triangles

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Geometry 5-5 Inequalities in Triangles

• Within a triangle
• the biggest side is opposite the biggest angle.
• the smallest side is opposite the smallest angle.

C
Smallest Biggest BC AB AC
?A ?C ?B
12
5
A
B
9
2
Examples

• List the sides from shortest to longest.
• List the angles from largest to smallest.

C
63
62
55
A
B
DF 23 DE 14 EF 12
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Constructing Triangles
The two shortest sides of a triangle must add up
to be greater than the third side.
3 3 gt 7Cannot make a ?
4 4 gt 7Can make a ?
4 3 gt 7Cannot make a ?
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Example

• Can the following sets of numbers be the sides of
  a triangle?

19, 10, 7
7, 9, 6.2
21, 8, 13
5
Example

• Find the range of values that could be the third
  side of a triangle.
• Given 6 and 15 Given 40 and 11