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Modellina
Pe: 2008-07-19T21:03:19+03:00 In: In:

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trapezul dreptunghic ABCD cu AB|| CD, m(A)=m(D)=90 grade are AD=12cm ,AB=24 si m(B)=45 grade.Se noteaza AD intersectat cu BC={M}.Se cere:
a)natura si aria tr MAB
b)sa se arate ca AC perpendicular pe BC
c)daca CE||AD , E apartine(AB) sa se arate ca [DE]=[AC] si DE perpendicular pe AC

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  1. dan
    expert (VI)

    Modellina wrote: trapezul dreptunghic ABCD cu AB|| CD, m(A)=m(D)=90 grade are AD=12cm ,AB=24 si m(B)=45 grade.Se noteaza AD intersectat cu BC={M}.Se cere:
    a)natura si aria tr MAB
    b)sa se arate ca AC perpendicular pe BC
    c)daca CE||AD , E apartine(AB) sa se arate ca [DE]=[AC] si DE perpendicular pe AC

    \rm{ a)...\\ m(\hat{B})=45^0 \Rightarrow m(\hat{AMB})=90^0-45^0=45^0\\ deci m(\hat{A})=90^0 si AM\eq{AB}\\ \Rightarrow |Delta{AMB}- dreptunghic isoscel !\\ c)...\\ CD\parallel{AB}\Rightarrow (t.f.a.) \frac{MD}{MA}=\frac{DC}{AB}=...\\ ...=\frac{12}{24}=\frac{DC}{24}\\ deci DC\eq{MD}\eq{DA}=12cm\\ CE\perp{AB}\Rightarrow CE\parallel{DA} \Rightarrow ADCE-patrat,\\ deci DE=AC si DE\perp{AC} fiind diagonalele unui patrat !\\ b)...\\ DC\parallel{AB} \Rightarrow \frac{MC}{MB}=\frac{1}{2}\\ deci AC-mediana in \Delta{MAB} \Rightarrow AC este si inaltime\\ => AC\perp{MB} !

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