Triangle Inequality Proven: Prove la + bl ≤ lal + lbl

[frap]

Homework Statement

I don't know if I'm posting in the right area, but here is the question:
From the inequality: la dot bl= lal lbl lcos(theta)l is less than or equal to lal lbl

Deduce the triangle inequality:
la + bl is less than or equal to lal +lbl

Homework Equations

The Attempt at a Solution

I am not even sure where to begin :(
I'm wondering if I could use numbers to prove it, but that doesn't seem right.

 

[Mathdope]

Sorry, misread. Think about (|a| + |b|)^2. You also have a property available to you that says |a|^2 = a dot a.

 

[Feldoh]

|a+b|^2 =(a+b)dot(a+b) is a very nice identity application.