Question

se considera un triunghi MNP .Demonstrati ca daca d (N, MP) =d (P, MN), atunci m (<MNP)=m (<MPN)
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Answer 1

Dem: -notam { E∈(MN)⇔PE⊥MN si F∈(MP)⇔NF⊥MP.
-observam ca d(N,MP)=NF iar d(P,MN)=PE.
[NF]≡[PE](i.p)
[NP]≡[NP](latura comuna)
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⇒(din cazul de congruenta I.C)⇒ΔNFP≡ΔPEN⇒[PF]≡[NE](1)⇒[ME]≡[MF](2).
-din (1) si (2) ⇒ [MN]≡[MP] adica ΔMNP-isoscel de aici concluzia.