6. In Fig. 5.10, if AC = BD, then prove that AB = CD.
From the figure given in the problem,
We can say that
AC = AB + BC and BD = BC + CD
Now,
It is given that AC = BD
Therefore,
AB + BC = BC + CD
Now, According to Euclid's axiom, when equals are subtracted from equals, the remainders are also equal. Subtracting BC from both sides.
We will get
AB + BC - BC = BC + CD - BC
AB = CD
Hence proved