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In the following figure, if AC = BD, then prove that AB = CD.

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From the figure, it can be observed that

AC = AB + BC

BD = BC + CD

It is given that AC = BD

AB + BC = BC + CD (1)

According to Euclid’s axiom, when equals are subtracted from equals, the remainders are also equal.

Subtracting BC from equation (1), we obtain

AB + BC − BC = BC + CD − BC

AB = CD

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