If in a right-angled triangle a perpendicular be drawn from the right angle to the base, the triangles adjoining the perpendicular are similar both to the whole and to one another.
Proof
The two sub-triangles each share an angle with the original (the
non-right angle at B or C) and both have a right angle (at the
foot of the altitude and at the apex), so they are equiangular with
the original by I.32, hence similar by VI.4. By transitivity (V.11)
they are similar to each other.