A point C lies between two points A and B, such that AC = CB. Prove that $A C = \frac{1}{2} A B$ .

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Solution

Given: A point C lies between two points A and B.
AC = CB
To prove: $A C = \frac{1}{2} A B$
Proof: Point C lies between two points A and B (given).
So, AC+ BC = AB.
$\Rightarrow A C + A C = A B . . . . . . . . . . . . . . [A C = B C] \Rightarrow 2 A C = A B \Rightarrow A C = \frac{1}{2} A B$
Hence proved.

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