If RX = SX, then X must be the midpoint of RS

Question

anonymous · Answer

Only if R and S are collinear with X.

anonymous · Answer

this is all the info im given and its either true or false

anonymous · Answer

Said another way, suppose RSX is an isosceles triangle.  RX = SX, but X is not the midpoint of RS.

anonymous · Answer

So, do you think it's true?

anonymous · Answer

well normally if it were true it would be written RX=XS

anonymous · Answer

Either way to write it is ok.  Do you think the initial statement is true?

anonymous · Answer

well, yes. as i have been given similar problem set up the whole course

anonymous · Answer

It isn't always true (see my counterexample above), so it is false.  There are cases where it is true, but it isn't true in general, since there is at least one example where it is false.  Get it?

anonymous · Answer

yes, i see.

anonymous · Answer

Good.  Do math every day.