tiffy06 tiffy06
  • 24-10-2020
  • Mathematics
contestada

given: y is the midpoint of XZ
prove: XY 1/2XZ​

Respuesta :

erinna erinna
  • 31-10-2020

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.

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