Synthetic Geometry Proofs:
The following, from Projectmaths.ie are excellent explanations of the Synthetic Geometry Proofs:
Theorem 11: If three parallel lines cut off equal segments on some transversal line, then they will cut off equal segments on any other transversal.
Theorem 12: Let ABC be a triangle. If a line l is parallel to BC and cuts [AB] in the ratio s : t, then it also cuts [AC] in the same ratio.
Theorem 13: If two triangles ABC and are similar, then their sides are proportional, in order: