Question

REPEDE VA ROG FRUMOS

Answer 1

$\it \Delta ABC-isoscel,\ \ AB=AC\ \ \ \ \ \ (*) \\ \\ \Big[ AD-\ bisectoare\ pentru\ \widehat A,\ D\in\ BC,\ \Rightarrow AD- median\breve a \Rightarrow \\ \\ \Rightarrow\ D\ - \ mijlocul\ lui\ [BC]\ \ \ \ \ \ (1)\\ \\ M\ -\ mijlocul\ lui\ [AB]\ \ \ \ \ \ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow DM\ -\ linie\ mijlocie \Rightarrow DM=\dfrac{AC}{2} \ \ \ \ \ \ \ \ \ \ \ \ (3)\\ \\ \\ Analog,\ DN\ -\ linie\ mijlocie \Rightarrow DN=\dfrac{AB}{2}\ \stackrel{(*)}{=}\ \dfrac{AC}{2}\ \ \ \ \ \ (4)$

$\it (3),\ (4) \Rightarrow DM=DN \Rightarrow\Delta DNM - isoscel$