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Converse of Basic Proportionality Theorem

Let A B be a ...

Question

Let be a segment with C and D between them such that the order of points on the segment is A, C, D,B. Suppose AD = BC. Prove that AC = DB.

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Solution

The points are arranged as shown below.

It is given that AD = BC

From the figure, we get:

AD = AC + CD and BC = CD + BD

AC + CD = CD + BD

AC = BD

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