Question

Answer 1

Kẻ \(AN\) cắt \(CD\) tại \(I\)

Xét \(\Delta ABN\&\Delta NCI:\)

\(\widehat{BNA}=\widehat{INC}\left(đối.đỉnh\right)\)

\(BN=NC\) (\(N\) là trung điểm \(BC\))

\(\widehat{ABN}=\widehat{NCI}\left(so.le.trong\right)\)

\(\Rightarrow\Delta ABN=\Delta NCI\left(g.c.g\right)\)

\(\Rightarrow AN=AI;AB=CI\)

mà \(MA=MD\) (\(M\) là trung điểm \(AD\))

\(\Rightarrow MN\) là đường trung bình \(\Delta ADI\left(1\right)\)

\(\Rightarrow MN//DI\) hay \(MN//CD\left(đpcm\right)\)

\(\left(1\right)\Rightarrow MN=\dfrac{DI}{2}\)

mà \(DI=CI+CD=AB+CD\left(AB=CI\left(cmt\right)\right)\)

\(\Rightarrow MN=\dfrac{AB+CD}{2}\left(đpcm\right)\)