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

4. If a point C lies between two points A and B such that AC = BC, then prove that

AC =1/2AB. Explain by drawing the figure.

Solution

Given that C is the lies between both points A and B

And

AC     = BC

Add AC both side we get

AC  + AC     = BC + AC

According to definition of Euclid , if equals are added to equals, whole will equal 

Here, (BC + AC) coincides with AB. It is known that things which coincide with one another are equal to one another.

2AC  = AB 

Divide by 2 we get

AC     = AB/2