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

User Tloach
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1 Answer

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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.​

User Encombe
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