First, note that vertices and are on opposite sides of line . Then either lies on , or does not. if does not, then it must lie on either side (half plane) of . In other words, and must be on the opposite sides of , or and must be on the opposite sides of . If and are on the opposite sides, has a non-empty intersection with . But if and are on the opposite sides, then and are on the same side, which means that does not intersect . ∎
Remark A companion property states that if line passes through one vertex of a triangle and at least one other point on , then it must intersect exactly one of the following:
Of course, if passes through , must lie on . Similarly, lies on if passes through .
|Date of creation||2013-03-22 15:32:09|
|Last modified on||2013-03-22 15:32:09|
|Last modified by||CWoo (3771)|