Axioms are not proved, theorems need to be proved, and this thing is a theorem and can be proved. After all, after being connected, it is an isosceles triangle, and the three lines of the isosceles triangle are unified. It is enough to prove that the midpoint or the high line is vertical first. This order is irrelevant, I hope I can help you.

This sentence, in turn, is the definition of the median vertical line, and the distance to both ends is the same. This sentence is the nature and application of the perpendicular line, so it needs to be proved, and it must be a theorem.