8. (4 points) A triangle is divided into 1000 triangles. What is the minimum number of distinct points at which the vertices of these triangles can be located?
Answer: 503

Solution: The sum of the angles of a triangle is $180^{\circ}$, so for a thousand triangles, it is $180000^{\circ}$. Where did the extra $179820^{\circ}$ come from? Each internal vertex where only the angles of triangles meet adds $360^{\circ}$. Each vertex on the side of the original triangle or on the side of one of the triangles in the partition adds $180^{\circ}$. To achieve the minimum, we need as many points of the first type as possible. $179820: 360=499.5$. Therefore, we need 499 points of the first type and one point of the second type. The example is constructed by sequentially adding new points inside (not on the boundary) of the existing triangles and one point on the boundary.

Adding the three vertices of the original triangle, we get the answer 503.