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

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

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

Example

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

19, 10, 7

21, 8, 13

7, 9, 6.2

Example

Find the range of values that could be the third side of a triangle.

Given: 6 and 15 Given: 40 and 11