Let $\theta >0$ be unknown and suppose that $(X,Y)$ is uniform over the triangular region with vertices at $(0,0)$,$(\theta, 0)$, and $(0,\theta)$. Let $(X_i,Y_i)$ be iid as $(X,Y)$. Find a one dimensional sufficient statistic $T$ for $\theta$, and prove it's sufficient.
My thoughts: I want to find the likelihood function then try to separate as two functions so that I can get a statistic, but in this case, I have difficulty finding the density function. Any hints would be appreciated.