Question

Prove that every line segment has one and only one mid point . State the Euclid axiom used

Answer 1

$\textbf{\huge{\underline{ Hello Mate! }}}$

Given : The given figure is a line.

To Prove : Every line has single mid point.

Proof : Let C and D both be the mid point.

This means that,

AC = BC ( Since C is midpoint ) __(1)

and, AD = BD ( Since D is midpoint ) ___(2)

Subtracting (1) from (2)

AD - AC = BD - BC

CD = - CD

CD + CD = 0

This means that point C and D overlap each other and hence there can be only one midpoint i.e. C.

$\textbf{ Have great future ahead! }$