If a point $ C $ lies between two points $ A $ and $ B $ such that $ A C=B C $, then prove that $ \mathrm{AC}=\frac{1}{2} \mathrm{AB} $. Explain by drawing the figure.
Given:
A point $C$ lies between two points $A$ and $B$ such that $AC=BC$.
To do:
We have to prove that $AC=\frac{1}{2}AB$.
Solution:
Given,
$AC=BC$
By adding $AC$ on both sides we get,
$AC+AC=BC+AC$
This implies,
$2AC=BC+AC$ ($BC+AC$ coincides with $AB$)
According to Euclid's Axiom $4$
$BC+AC=AB$.
Therefore,
$2AC=AB$
This implies,
$AC=\frac{1}{2}AB$
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