The altitude and median of an isosceles triangle _________.

Consider an isosceles triangle $△ABC$. 

We know that a line that is drawn perpendicularly from one vertex of a triangle to the opposite side is defined as the altitude of a triangle.

The median of a triangle is a line segment that bisects one side by connecting a vertex to the opposing side's midway.

Draw the median and altitude of an isosceles triangle.

Let us draw a line segment AL that is perpendicular to BC, then AL is an altitude for this $△\mathrm{ABC}$ _.

We can see that the length of BL and LC is also the same. 

Therefore, AL is a median of this triangle as well.

Therefore, AL is altitude and also the median of $△\mathrm{ABC}$,  this suggests that it coincides.