Medium
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.
(N/A) Given: Point $C$ lies between $A$ and $B$ such that $AC = BC$.
To prove: $AC = \frac{1}{2} AB$.
Proof:
Since $C$ lies between $A$ and $B$,we have $AC + BC = AB$.
Given that $AC = BC$.
Substituting $AC$ for $BC$ in the equation $AC + BC = AB$,we get:
$AC + AC = AB$
$2 AC = AB$
Dividing both sides by $2$,we get:
$AC = \frac{1}{2} AB$.
Hence proved.
To prove: $AC = \frac{1}{2} AB$.
Proof:
Since $C$ lies between $A$ and $B$,we have $AC + BC = AB$.
Given that $AC = BC$.
Substituting $AC$ for $BC$ in the equation $AC + BC = AB$,we get:
$AC + AC = AB$
$2 AC = AB$
Dividing both sides by $2$,we get:
$AC = \frac{1}{2} AB$.
Hence proved.
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