Given:
Y is the midpoint of XZ.
To prove:
[tex]XY=\dfrac{1}{2}XZ[/tex]
Proof:
It is given that Y is the midpoint of XZ. It means Y divides the line segment XZ in two equal parts XY and YZ.
[tex]XY=YZ[/tex] ...(i)
Point Y lines on the segment XZ, so by segment addition theorem, we get
[tex]XY+YZ=XZ[/tex]
[tex]XY+XY=XZ[/tex] [tex][Using (i)][/tex]
[tex]2XY=XZ[/tex]
Divide both sides by 2.
[tex]XY=\dfrac{1}{2}XZ[/tex]
Hence proved.
