geometry 5-5 inequalities in triangles within a triangle: – the biggest side is opposite the...
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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.
A B
C
Smallest Biggest BC AB AC ∠A ∠C ∠B
125
9
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Examples• List the sides from shortest to longest.
• List the angles from largest to smallest.
A B
C
55° 62°
63°
DF = 23DE = 14EF = 12
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Constructing TrianglesThe two shortest sides of a triangle must add up to be greater than the third side.
74 3
4 +4 > 7Can make a Δ
3 +3 > 7Cannot make a Δ
4 +3 > 7Cannot make a Δ
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Example
• Can the following sets of numbers be the sides of a triangle?
19, 10, 7
21, 8, 13
7, 9, 6.2
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Example
Find the range of values that could be the third side of a triangle.
Given: 6 and 15 Given: 40 and 11