O.VI.27

[Andi Brojbeanu]

Triunghiurile \( \bigtriangleup{ABC} \) si \( \bigtriangleup{CDA} \) sunt congruente, iar \( [AC]\cap[BD]=\emptyset \). Fie \( M, N\in [AC], M\neq N \), astfel incat \( AM=CN \). Stabiliti daca \( \triangle{DMN}\equiv\triangle{BNM} \).

Probleme date la olimpiade, RMT 1/1998

[salazar]

\( \triangle ABC\equiv\triangle CDA\Longrightarrow BC=DA,\angle DAC\equiv\angle BCA \).
\( \triangle DAM\equiv\triangle BCN\Longrightarrow DM=BN \).
\( \triangle DAN\equiv\triangle BCM\Longrightarrow DN=BM \).
-finalizare:\( \triangle DMN\equiv\triangle BNM(LLL) \).