Question

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

Answer 1

Prove the given expression

Given, $AC=BC$

and, $C$ lies between $A$ and $B$, so $AB=AC+BC$

Now,

Add $AC$ to both sides of the given equation

$AC+AC=AC+BC$

$2AC=AB$ $...(\because AB=AC+BC)$

$\therefore$ $AC=\frac{1}{2}AB$

Hence proved.