  The \emph{Hosoya triangle} is a triangular array where every entry is a
product of two Fibonacci numbers. We use the geometry of this triangle to find
new identities related to Fibonacci numbers. We give geometric interpretation
for some well-known identities of Fibonacci numbers. For instance, the Cassini
identity and the Catalan identity. We also extend some identities that hold in
the Pascal triangle to the Hosoya triangle. For instance, the hockey stick
extends from binomials to products of Fibonacci numbers and the rhombus
property extends a binomial identity from the Pascal triangle to an identity of
products of Fibonacci numbers in the Hosoya triangle.
