If a point C lies between two points A and B such that AC = BC, then prove that AC = ½ AB. Explain by drawing the figure.

Solution:

Given that, AC = BC

Now, adding AC both sides.

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 = (½)AB.