Răspuns:
Explicație pas cu pas:
2)
a)
ΔABC= echilateral →AB≡BC≡AC→∡A=∡B=∡C= 60°
ΔMPC= echilateral →MP≡PC≡MC→∡MCP=∡PMC= MPC=60°
BM= MC
ΔBMP- BM≡MP(isoscel)
-∡BMP=180-60 =120°
- MBP≡MPB= (180-120):2= 30°
∡ABC= 60°
∡MBP=30°
∡ABP= 60+30=90°→AB⊥BP
-
∡CPM= 60°
∡MPB= 30°
∡BPC= 60+30
∡BPC= 90°→CP⊥BP
-
CP⊥BP
AB⊥CP
↓
CP║AB ( doua drepte perpendiculare pe aceiasi dreapta sunt paralele )
-
-
b)
∡ABP= ∡ABC+∡CBP
∡ABP= 60+30
∡ABP= 90°
-
-
c)
∡BMT=∡NMC= 30°(unghiuri opuse la varf)
Ptrulaterul ABNM - ∡A=60°
-∡ B= 60°
- ANM= 90°( MN⊥AC )
-∡ BMN=360-( 60-60-90)= 150°
∡NMT= ∡NMB+ ∡BMT
∡NMT= 150+30
∡NMT= 180°→ N,M ,T - coliniare
