1 ) 

$\left. \begin{align}
  & \frac{MA}{MC}=\frac{CP}{AP} \\
 & \frac{MA}{MB}=\frac{QB}{AQ} \\
\end{align} \right\}\xrightarrow{MB=MC}\frac{AP}{PC}=\frac{AQ}{QB}\Rightarrow QP||BC$

2 ) 

$\left. \begin{align}
  & \frac{MA}{MC}=\frac{AP}{PC} \\
 & \frac{MA}{MB}=\frac{AQ}{QB} \\
\end{align} \right\}\xrightarrow{MB=MC}\frac{AP}{PC}=\frac{AQ}{QB}\Rightarrow MP||AB$

3 ) 

$\left. \begin{align}
  & \frac{MA}{MC}=\frac{AP}{PC} \\
 & \frac{MA}{MB}=\frac{AQ}{QB} \\
\end{align} \right\}\xrightarrow{MB=MC}\frac{AP}{PC}=\frac{AQ}{QB}\Rightarrow QP||BC$

4 ) 

$\left. \begin{align}
  & \frac{MA}{MC}=\frac{CP}{AP} \\
 & \frac{MA}{MB}=\frac{QB}{AQ} \\
\end{align} \right\}\xrightarrow{MB=MC}\frac{AP}{PC}=\frac{AQ}{QB}\Rightarrow QM||AC$