1. Section 5-5 Inequalities in triangles
GEOMETRY

2. Comparison Property of Inequality
If 𝑎=𝑏+𝑐 and 𝑐>0, then 𝑎>𝑏.
Given: 𝒂=𝒃+𝒄,𝒄>𝟎
Prove: 𝒂>𝒃
Statements
Reasons
1.)
2.)
3.)
4.)
5.)

3. Theorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.
𝑰𝒇 𝑿𝒁>𝑿𝒀, 𝒕𝒉𝒆𝒏 𝒎∠𝒀>𝒎∠𝒁.

4. Example 1: You are building a deck and want to put benches in the two largest corners, but which corners are the largest?

5. Theorem 5-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.
𝑰𝒇 𝒎∠𝑨>𝒎∠𝑩, 𝒕𝒉𝒆𝒏 𝑩𝑪>𝑨𝑪.

6. Example 2: Which side is shortest?

7. Theorem 5-12 (Triangle Inequality Thm): The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

8. Example 3:

9. Example 4:
The lengths of two sides of a triangle are given. Describe the lengths possible for the third side.
A B.