I need to prove that $d(y,z) + d(x,y) \geq d(x,z)$.

With $d(x,y) = \sqrt{(x\_1-y\_1)^2 + (x\_2-y\_2)^2}$. 

I'm struggling to figure out how to work with the square roots especially when they're over an addition problem. Any help is appreciated.

Edit: to make this simpler. I think all I need to do is figure out how to add $\sqrt{(x\_1-y\_1)^2 + (x\_2-y\_2)^2}$ + $\sqrt{(y\_1-z\_1)^2 + (y\_2-z\_2)^2}$. Then I can do the a + b proof method. But I just can't figure out how to add those equations so it ends up equalling $\sqrt{(x\_1-z\_1)^2 + (x\_2-z\_2)^2}$.