Question

Given: y is the midpoint of. XZprove: XY 1/2XZ

Answer 1

The midpoint by definition is the divides a line segment in two.

This means if point Y is the midpoint of XZ, then it is equidistant from X and Z which means

`XY=YZ`

And since from segment addition postulate, we know that

`XY+YZ=XZ`

substituting XY = YZ in the above equation gives

`XY+XY=XZ`
`\rightarrow2XY=XZ`
`\therefore XY=(1)/(2)XZ.`

Hence, it is proved that if Y is the midpoint of XZ then XY = 1/2XZ.​