Question

Fie ABCD un patrulater.​ Dacă MA + MC = MB + MD

Answer 1

Răspuns:

da, asa este, asa mi-a dat si mie, tot paralelogram!!!!

Explicație pas cu pas:

MA+MB=MC+MD

MA-MD=MC-MB

(detaliez putin , pt aducetre aminte MO+OA-MO-OD=OA-OD=-OD+OA=DO+OA-DA, tot vectori)

DA=BC

DA si BC egali in   modyul, aceesi directie si sensuri opuse

ABCD -paralelogram (in cartezian)

as simple as that!!!

Answer 2

$\it \overrightarrow{MA}+\overrightarrow{MC}=\overrightarrow{MB}+\overrightarrow{MD} \Rightarrow \overrightarrow{MA}-\overrightarrow{MB}=\overrightarrow{MD}-\overrightarrow{MC} \Rightarrow\\ \\ \\ \Rightarrow\overrightarrow{BA}=\overrightarrow{CD} \Rightarrow \begin{cases} \it BA||CD\\ \\ [BA]\equiv[CD]\end{cases} \Rightarrow ABCD-\ paralelogram$