  We study the evaporation of two-dimensional black holes in JT gravity from a
three-dimensional point of view. A partial dimensional reduction of AdS$_3$ in
Poincar\'e coordinates leads to an extremal 2D black hole in JT gravity coupled
to a 'bath': the holographic dual of the remainder of the 3D spacetime.
Partially reducing the BTZ black hole gives us the finite temperature version.
We compute the entropy of the radiation using geodesics in the
three-dimensional spacetime. We then focus on the finite temperature case and
describe the dynamics by introducing time-dependence into the parameter
controlling the reduction. The energy of the black hole decreases linearly as
we slowly move the dividing line between black hole and bath. Through a
re-scaling of the BTZ parameters we map this to the more canonical picture of
exponential evaporation. Finally, studying the entropy of the radiation over
time leads to a geometric representation of the Page curve. The appearance of
the island region is explained in a natural and intuitive fashion.
