Given a triangle ABC where point D is inside the triangle and line segments AD, BD, and CD are extended to intersect the sides BC, AC, and AB respectively at points E, F, and G, show how applying Ceva's Theorem can determine if the cevians AD, BD, and CD

Ceva’s Theorem states that for cevians AD, BE, and CF of triangle ABC to be concurrent, the product of the ratios of the divided segments must equal 1: (AF/FB) * (BD/DC) * (CE/EA) = 1. To prove Ceva’s Theorem, consider the areas of triangles formed by cevians and use the ratio of areas to establish the necessary equality.

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