Ceva’s Theorem and its Converse(without proof)
Ceva’s Theorem is a fundamental theorem related to triangles. It was proved by an Italian mathematician Giovanni Ceva. Even though he may not have been the first to prove it, the theorem still bears his name. I will write about one of many (pdf file) proofs of Ceva’s theorem and its converse in some other related post. This post is all about understanding the patterns in the mathematical relation given by the theorem . A cevian is a line segment joining a vertex of a triangle to any point on the line which contains the opposite side of the vertex. A cevian can lie outside of a triangle too, which we generally find in the case of obtuse angled triangles. ( NOTE : Is the line segment overlapping an edge of a triangle a cevian? I have attempted to answer this question at the end of this post.) Sometimes a cevian is also defined as a line(instead of a segment) that passes through a vertex and cuts the line which contains the side opposite to the vertex. In △ABC in the...