If, in a right-angled triangle, a (straight line) is drawn from the right angle perpendicular to the base then the triangles around the perpendicular are similar to the whole (triangle), and to one another. * Let $ABC$ be a right-angled triangle having the angle $BAC$ a right angle, and let $AD$ have been drawn from $A$, perpendicular to $BC$ [Prop. 1.12]. * I say that triangles $ABD$ and $ADC$ are each similar to the whole (triangle) $ABC$ and, further, to one another.
If in a right-angled triangle a straight line is drawn from the vertex of the right angle to the hypotenuse, then the resulting two triangles are similar.