Question

Dever. Sendo M e N pontos medios de AD e BC prove que: EF=(B-b)/2 e MN=(B+b)/2​

Answer 1

Resposta:

Explicação passo a passo:

chamando CD  de B

chamando AB  de b

ΔADC ≈ ΔAMF

CD/MF = 2DM/DM  ⇒ CD/MF = 2 ⇒ MF = CD/2 ⇒ MF = B/2

ΔABC ≈ ΔFNC

AB/FN = 2CN/CN ⇒ AB/FN = 2 ⇒ FN = AB/2 ⇒ FN = b/2

MN =  MF + FN ⇒ MN = B/2 + b/2 ⇒ MN = (B + b)/2

ΔABD ≈ ΔMED

AB/ME = 2MD/MD ⇒ AB/ME = 2 ⇒ ME = AB/2 ⇒ ME = b/2

ΔABC ≈ ΔFNC

AB/FN = 2NC/NC ⇒ AB/FN = 2 ⇒ FN = AB/2 ⇒ FN = b/2

observando

EF =  MN - (ME + FN)

EF = (B  + b)/2 - (b/2 + b/2)

EF = (B + b)/2 - (b)

EF = (B + b - 2b)/2

EF = (B - b)/2