6.  In Fig. 5.10, if AC = BD, then prove that AB = CD.

      

Answers (1)

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 

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