Question 169
Given $ABC$ an acute triangle with $AB \lt AC$, let $AD$ be the altitude and $AE$ the angle bisector, where $D, E \in (BC)$. Given the acute triangle $A'B'C'$, with $A'B' \lt A'C'$, let $A'D'$ be the altitude and $A'E'$ the angle bisector, where $D', E' \in (B'C')$.
If $[AB] \equiv [A'B']$, $[AD] \equiv [A'D']$ and $[AE] \equiv [A'E']$, prove that triangles $ABC$ and $A'B'C'$ are congruent.
If $[AB] \equiv [A'B']$, $[AD] \equiv [A'D']$ and $[AE] \equiv [A'E']$, prove that triangles $ABC$ and $A'B'C'$ are congruent.