THE THEOREM OF MENELAUS AND ITS APPLICATION TO SOLVING GEOMETRIC PROBLEMS

Annotatsiya

Abstract. This article analyzes the theorem of Menelaus, one of the fundamental results of classical synthetic geometry, and examines its practical applications to geometric problems of varying complexity: proving the collinearity of points, finding ratios of segments, and solving olympiad-level problems. The proof of the theorem, its relation to Ceva’s theorem, and several representative examples are discussed in detail. The results show that using Menelaus’ theorem increases the efficiency of problem-solving in school and university geometry courses, offering a shorter and more elegant alternative to coordinate-based methods.