Verified answer

It is trivially true.

d(u,v) ≥ 0

if you add it to d(u,w) you will get

d(u, w) ≤ d(u, v) + d(u, w)

if you had meant to ask about:

d(u, w) ≤ d(u, v) + d(v, w)

this is true since the shortest distance between two points is a straight line

d(u, w) ≤ d(u, v) + d(v, w)

you can also use pythagoras' theorem or the distance formula for these three distances.