Do all medians of a isosceles triangle bisect it's sides?

You have a confusion here! Let's take a look at the definition of median. > Median: A line joining the vertex of a triangle with the mid-point of the opposite side. So, by definition, every median does bisect it's base. read more

The reverse is also true. Consider a triangle ABC: – If angle bisector of vertex A is also the median, the triangle is isosceles such that AB = AC and BC is the base. Hence this angle bisector is also the altitude. – If altitude drawn from vertex A is also the median, the triangle is isosceles such that AB = AC and BC is the base. read more

In general, altitudes, medians, and angle bisectors are different segments. In certain triangles, though, they can be the same segments. In Figure , the altitude drawn from the vertex angle of an isosceles triangle can be proven to be a median as well as an angle bisector. read more