Lines Through Endpoints of One Side of Triangle to Point Inside Triangle is Less than Sum of Other Sides/Corollary

Theorem
The angle between the two line segments from the endpoints of one side to a point inside the triangle is greater than the angle between the other two sides of the triangle.

Proof

 * Point Inside Triangle.png

From External Angle of Triangle is Greater than Internal Opposite:
 * $\angle BDC > \angle CED$

Similarly:
 * $\angle CEB > \angle BEC$

Since $\angle CED$ is the same angle as $\angle CEB$:
 * $\angle BDC > \angle CEB > \angle BEC$