Question

se considera patratul efgh si punctele m apartine ef, n apartune fg , p aparteine gh si q apartine he astfel incat em congruent cu fn congruent gp conruent cu hq ..arati ca mnpq este patrat!Daca poti sa imi arati si figura cum o faci

Answer 1

AB=BC=CD=AD si EM=FN=PG=HQ ⇒ MF=NG=PH=EQ
Comparam ΔEMQ cu Δ FNM cu Δ GPN cu Δ HQP dreptunghice
EM=FN=PG=HQ
MF=NG=PH=EQ⇒ CC  ⇒ΔEMQ ≡ Δ FNM ≡ Δ GPN ≡Δ HQP
⇒MQ=QP=PN=MN ⇒ MNPQ- romb

∡EMF=180°
∡EMQ+∡QMN+∡NMF=180°
∡EMQ+∡NMF =90° ⇒ ∡QMN=90°

⇒ MNPQ -patrat