4.  If a point C lies between two points A and B such that AC = BC, then prove that AC = 1/2  AB. Explain by drawing the figure.

Answers (1)

It is given that
AC = BC 
Now,

In the figure given above, AB coincides with AC + BC.
Also, Euclid’s Axiom (4) says that things which coincide with one another are equal to one another. So, it can be deduced that AC + BC = AB
Now,
2AC = AB                                        (\because AC = BC )
Therefore,
AC = \frac{1}{2}AB
Hence proved 

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