Any pyramid which has a triangular base is divided into two pyramids equal and similar to one another, similar to the whole, and having triangular bases, and into two equal prisms; and the two prisms are greater than the half of the whole pyramid.
Proof
Bisect each edge (I.10); the midpoint cuts split the pyramid into
two corner pyramids and two prisms. The two corner pyramids are
similar to the original (their edges halved), and by I.34 the two
prisms are congruent.