Transcript Geometry 5-5 Triangle Inequalities

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