Coded triangle numbers
The n(th) term of the sequence of triangle numbers is given by, tn =
½n(n+1); so the first ten triangle numbers are:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

By converting each letter in a word to a number corresponding to its
alphabetical position and adding these values we form a word value. For
example, the word value for SKY is 19 + 11 + 25 = 55 = t(10). If the
word value is a triangle number then we shall call the word a triangle
word.

Using words.txt (right click and 'Save Link/Target As...'), a 16K text
file containing nearly two-thousand common English words, how many are
triangle words?