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)