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

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

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Given that, AC = BC

L.H.S + AC = R.H.S + AC

AC + AC = BC + AC

2AC = BC + AC

We know that, BC + AC = AB (as it coincides with line segment AB)

∴ 2 AC = AB (If equals are added to equals, the wholes are equal.)

⇒ AC = ($$\frac{1}{2}$$)AB.

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