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# 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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