Although there are various and interesting proofs for the concurrency of the altitudes and medians of a triangle, no proof seems to have been provided for these theorems, which use the concept of loci. In this paper, we prove these two theorems by using loci, first showing that every altitude and median of a triangle is a locus of some interesting points in the plane or inside the triangle. With the same method, we provide new proofs for the theorems of Carnot and Ceva.
