Question
Mathematics Question on Euclid’s Definitions, Axioms and Postulates
In Fig. 5.10, if AC = BD, then prove that AB = CD.
Answer
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