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.