Theorem 2.10: Let   A,   B,   and   C   be three noncolinear points. If   D   is on the line through   A   which is parallel to   BC,   then there is a real number   s   such that

Proof: If   A = D,   then we can take   s = 0,   and we're done. So we can assume that   D   is a different point than   A.

Let

and

There are three cases:

• BC   is horizontal
• BC   is vertical
• BC   is neither horizontal nor vertical.

next theorem (2.11)