BD si AC diagonale,
AE si BG inaltimi (AE =BG)
a) In Δ ADE, m(<D)=m(<A) = 45 grade ⇒Δ ADE isoscel (DE=AE)
Notam EF inaltimea dusa din E pe AD
EF = AD/2 = 4√2/2 = 2√2
In Δ DEF:
m(<D) = m(<E) = 45 grade ⇒ Δ DEF isoscel (DF = EF=2√2)
DE² = FD² +FE²
DE² = (2√2)²+(2√2)²
DE² = 16
DE = 4
DE=GC=4 ⇒ AB =EG = 10-8 =2
b) BD=AC = diagonale
DE=AE=GC=BG=4
In Δ BDG :
BG=4
DG = DE+EG = 4 +2 =6
BD² =BG² +DG²
BD² = 16 +36
BD² =52
BD = 2√13
BD = AC = 2√13
