Question

Trapezul ABCD are bazele AB si CD egale cu 20 cm si respectiv 15 cm , iar diagonalele AC=28 si BD=35.Stiind ca AC Π BC ={O}, calculati : OA , OB,OC, OD. [se foloseste teorema fundamentala a asemanarii] Π = intersectat

Answer 1

deoarece AB||DC si 
∧DCA≡∧CAB
∧ABD≡∧BDC
∧DOC ≡∧AOB-opuse la varf
⇒ΔDOC≈ΔAOB⇒
AO/OC=OB/DO=AB/DC
(AC-OC)/OC=(BD-DO)/DO=20/15=4/3
luand cate 2 fractii obtinem
28/OC -1=4/3
28/OC=4/3+1=7/4
OC=28.4/7=16 cm⇒OA=28-16=12 cm
35/DO-1=4/3
35/DO=7/4
DO=35.4/7=20 cm⇒OB=35-20=15 cm