How do we prove that BC is true using a proof by contradiction method?

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Paul · Answer

Proving (BC) by Contradiction         To prove that BC is true using a proof by contradiction method, we start by assuming that BC is not true, i.e., B is connected to some point other than C. Let's name this point as E, so that BE and EC exist.         Next, we consider two triangles ΔADE and ΔBCE. We know that:                      AD = BC [Given]             AE = BE + AD [Triangle inequality]             AC = AE + EC [Triangle inequality]             BC = EC + BE [Triangle inequality]                  By analyzing the relationships between the sides of these triangles and the collinearity of points A, B, and C, we can arrive at a contradiction. This contradiction ultimately proves that BC is indeed true.

Proving (BC) by Contradiction

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