# This exercise contains an outline of a proof that the Theorem of Menelaus implies Cevas Theorem….

This exercise contains an outline of a proof that the Theorem of Menelaus implies Cevas Theorem. Suppose ^ABC is a triangle and ('AL , ('BM, and ('CN are three proper Cevian lines. (a) Assume, first, that the three Cevian lines are concurrent at a point P. Apply the Theorem of Menelaus to each of the triangles ^ABL and ^ALC. Combine the results to derive the formula in Cevas Theorem. (b) Now assume that the formula in Cevas Theorem holds. If the three Cevian lines are not mutually parallel, then it may be assumed that ('AL and ('BM intersect. Let P

This exercise contains an outline of a proof that the Theorem of Menelaus implies Cevas Theorem. Suppose ^ABC is a triangle and ('AL , ('BM, and ('CN are three proper Cevian lines. (a) Assume, first, that the three Cevian lines are concurrent at a point P. Apply the Theorem of Menelaus to each of the triangles ^ABL and ^ALC. Combine the results to derive the formula in Cevas Theorem. (b) Now assume that the formula in Cevas Theorem holds. If the three Cevian lines are not mutually parallel, then it may be assumed that ('AL and ('BM intersect. Let P be the point at which ('AL and ('BM intersect and let N be the point at which ('CP intersects ('AB . Use Exercise 14(a) to prove that N D N.