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The orbit closure of the unfolding of every rational right and isoscelestriangle is computed and the asymptotic number of periodic billiardtrajectories in these triangles is deduced. This follows by classifying allorbit closures of rank at least two in hyperelliptic components of strata ofAbelian and quadratic differentials. Additionally, given a fixed set of angles,the orbit closure of the unfolding of all unit area rational parallelograms,isosceles trapezoids, and right trapezoids outside of a discrete set isdetermined.

Billiards in right triangles and orbit closures in genus zero strata