Question

Exercitiile 12,13,14 !!VA rog ajutati-ma,dau coronita

Answer 1

14)
AB=√BD×BC
AD=√BD×DC
AC=√DC×BC
AB*AD*AC=√BD×BC×√BD×DC×√DC×BC=√BD²×BC²×CD²=BD×BC×CD



13)
AD=4
DB=8
AB=AC=4+8=12
CD=√(12²-4²)=√(144-16)=√128=8√2
A=12×8√2/2=48√2 cm²

12.
ducem inaltimile din MA si NB 
notam MN=x     si QA=BP=y
 QP=x+2y
A=(x+x+2y)×4/2= 32    2(x+y)×2=32      x+y=8
teorema inaltimii in triunghiul dreptunghic NBP
NB=√QB×BP    NB²=QB×BP
4²=(y+x)y    dar x+y=8
16=8y    y=2 x=6
deci MN=6 cm si PQ=2+6+2=10 cm


15.
AD=√BD×CD
AD²=BD×CD
putem scrie rapoartele  AD/CD=BD/AD  asta inseamna ca
Δ ADB~ΔDCA ⇒ ∡ABD≡∡DAC  si ∡BAD≡∡ACD 
dar    ∡ABD+∡BAD=90°  ⇒ ∡BAD+∡DAC=90°⇒∡BAC=90°