One picture, many identities: visual proof templates across number triangles

We present visual proof templates based on arrow-chasing arguments in Pascal's triangle. Starting from familiar binomial identities, such as the hockey-stick theorem or the classical formula for the sum of binomial squares, we show how the same diagrammatic configurations can be adapted to other recursive number triangles, including the Bell, Catalan, and Stirling triangles. These templates highlight structural similarities across different combinatorial settings and support the transfer of summation arguments beyond their original context. The emphasis is on geometric insight rather than on deriving new formulas.