Question

Cho tam giác ABC, Gọi M, N, P lần lượt là trung điểm của AB, BC, CA. Chứng minh rằng :

a, \(\overrightarrow{\text{Ạ}N}=\overrightarrow{AM}+\overrightarrow{AP}\)

b, \(\overrightarrow{AN}+\overrightarrow{BP}+\overrightarrow{CM}=\overrightarrow{0}\)

Answer 1

\(\overrightarrow{AN}=\frac{\overrightarrow{AB}+\overrightarrow{AC}}{2}=\frac{\overrightarrow{AB}}{2}+\frac{\overrightarrow{AC}}{2}=\overrightarrow{AM}+\overrightarrow{AP}\)

\(\overrightarrow{AN}=\frac{\overrightarrow{AB}+\overrightarrow{AC}}{2}\)

\(\overrightarrow{BP}=\frac{\overrightarrow{BA}+\overrightarrow{BC}}{2}\)

\(\overrightarrow{CM}=\frac{\overrightarrow{CB}+\overrightarrow{CA}}{2}\)

\(\Rightarrow\overrightarrow{AN}+\overrightarrow{BP}+\overrightarrow{CM}=\frac{\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{BA}+\overrightarrow{CA}+\overrightarrow{BC}+\overrightarrow{CB}}{2}=\overrightarrow{0}\)