Coded triangle numbers

The n\( ^{th} \) term of the sequence of triangle numbers is given by, \( t_n=\frac{1}{2}n(n+1) \); 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?