Isoceles: median, altitude, bisector coincide

Dependencies: SAS congruence, Linear pair sums to 180°, and Protractor axiom (Angle bisector exists and is unique).

Statement

Let $\triangle ABC$ satisfy $AB = AC$ (i.e. isosceles, with $A$ the apex and $BC$ the base). Then, starting from $A$, the bisector of the apex angle, the median to the base, and the altitude to the base are one and the same segment; if we call its endpoint on the base $D$, then $D$ simultaneously satisfies