Question

Draw a median on the non congruent side of an isosceles triangle. Is it the altitude or an angle bisector too?
If true then enter $1$ and if false then enter $0$

Answer 1

Consider triangle ABC, with AB = AC and AH perpendicular to BC.
Now, In triangle ABH and AHC,
$AH=AH$ (Common)
$\angle ABH=\angle ACH$ (Isosclees triangle property)
$\angle AHB=\angle AHC={90}^{\circ }$ ($AH\perp BC$)
Thus, $△AHB\cong △AHC$
$\angle BAH=\angle CAH$ (By cpct)
Thus, AH bisects $\angle A$