Question

If a point C lies between two points A and B such that AC=BC, then point C is called the midpoint of line segment AB. Prove that every line segment has one and only one midpoint.

Answer 1

given, c is a point
to prove, that every line segment has one and only one mid point

proof:
if possible let us take c and s are two different mid point of AB

If c is the mid point
ac=1/2AB
=> 2AC=AB----------(1)
if D is the mid point of AB
AD=1/2AB
=>2AD=AB--------(2)
FROM 1 and 2 ,we get
=> 2AC=2AD
=> AC =AB

FROM EUCLID'S AXIOM
6) things which are double of the same things are equal to one another
AC=ABDD IS POSSIBLE only when both the points CD are coincide

so our assumption is wrong
hence, every line segment has one and only one mid point

Answer 2

Answer:

point Cis aid point of line segment AB prove that every line segment one and only mid point