In Fig. 5.10, if AC = BD, then prove that AB = CD.
Given: AC = BD
From the figure,
AC = AB + BC
BD = BC + CD
AB + BC = BC + CD
According to Euclid’s axiom,
When two equals are subtracted from equals, remainders are also equal.
Subtracting BC both sides,
AB + BC – BC = BC + CD – BC
AB = CD
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