The median is the straight line connecting the top of the triangle (point A in your case) and the middle of the opposite side (side – BC, its middle – point M).
So, in order to build a median, you need to find the middle of BC using a ruler and connect the resulting point with vertex A.
And yes, there is a property for the median in isosceles triangles (it is also the bisector and height). But this works only if the median is drawn to the base (AC), and in this case, from point A, the median can only be lowered to the edge (BC).
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