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In Figure, if AC = BD, then prove that AB = CD.

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In Figure, if AC = BD, then prove that AB = CD.

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It is given, AC = BD

From the given figure, we get,

AC = AB + BC

BD = BC + CD

⇒ AB + BC = BC + CD [AC = BD, given]

We know that, according to Euclid’s axiom, when equals are subtracted from equals, remainders are also equal.

Subtracting BC from the L.H.S and R.H.S of the equation AB + BC = BC + CD, we get,

AB + BC - BC = BC + CD - BC

AB = CD

Hence Proved.

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