Question

In trapezul isoscel ABCD , cu AB||CD , se cunoaste ca AD=DC=BC si AB = 2 DC . Determinati masurile unghiurilor trapezului.

Answer 1

AB=2DC => [AE]≡[DC], AE║DC => AECD=paralelogr., [AD]≡[DC]

} => AECD=romb => [CE]=[AD] [AD]≡[CE]=>[CE]≡[BE]≡[BC] => ΔBCE=ech =>m(∡CBE)=60°     

ABCD=tr. is. => m(∡A)=m(∡B)=60°
m(∡D)=m(∡C)=180°-60°=120°

Mica verificare: m(∡A)+m(∡C)=60°+120°=180°
m(∡B)+m(∡D)=60°+120°=180° (∡A, ∡C, respectiv ∡B si ∡D suplementare)

Sper ca te-am ajutat!