This question is an exact duplicate of:
Prove Proposition 3.9: If a ray r emanating from an exterior point of triangle $ABC$ intersects side $AB$ at any point between $A$ and $B$, then $r$ also intersects side $AC$ or side $BC$.
Can someone help me finish this proof I started
By the hypothesis, let $DE$ be a ray emanating from an exterior point $D$ of triangle $ABC$ where the ray $DE$ intersects $AB$ at point $E$ such that $A*E*B$.
By pachs theorem, the line DE either intersects $AC$ or $BC$. 3.Suppose $DE$ intersects $AC$ at point $M$ where $M$ is not equal to $A$ Then by the definition of line segment, either $M=C$, or $D*M*E$