Question

If in triangle $XYZ,XY=XZ$ and $M,N$ are the mid points of $XY,YZ,$ then which one of the following is correct?

• A. $MN=YZ$
• B. $NY=NZ=MN$
• C. $MX=MY=NY$
• D. $MN=MX=MY$

Answer 1

The correct option is D $MN=MX=MY$

Since $M$ and $N$ are the mid-points of $XY$ and $YZ$ respectively,

therefore by midpoint theorem,

$MN$ is parallel to $XZ$ and $MN=\frac{1}{2}XZ=\frac{1}{2}XY$ $($since $XY=XZ)$

or $MN=MX=MY.$