Gas Fireplace Starter

Statement

To attack this problem well there are several approaches, but I have been very useful by the fact that the centroid is exactly twice as far from the vertex to the midpoint of the opposite side.

This fact is also used to show that the three medians intersect at a single point.

The idea is to draw the segments perpendicular to the line, not only from the vertices, if not from the midpoints of the sides.

line and perpendicular Baricentro

In our picture, the vertex that is separated from the other by the line I call A, and two B and C. Obviously, A 1, which is the midpoint of segment AB is on the same side as B and C and B and C _{1 1} are on the same side as A, because if the line could not pass the cutoff.

Now, by similarity, we have the segment from C is twice that of C ₁ , that of B is twice that of B ₁ and A is twice that of ₁ .

As the midpoints of the segments divided into two equal parts on the sides, the segments defined with respect to our line also play a special relationship. Indeed, it is easy to see that the segment unless the segment of B ₁ is exactly like the B segment _{1 More} segment C. Likewise, the segment of B minus 1 A segment worth the same as the segment of A ₁ less than C, and the segment of A less than C ₁ worth the same as the of B plus C ₁ .

Let us now try to show the equality that we demand. We start from the sum of the segments B and C. As we have seen that the segment of B plus C ₁ is equal to A less than B ₁ , we need the segment of C is equal to the segment unless the segment twice ₁ B . Therefore, the sum of the segments B and C is equal to the sum of B plus A least twice the segment B 1 . But we also know that the segment of B is exactly twice that of B ₁ therefore conclude that the sum of the segments B and C matches that of A.