Consider the figure given below.
 
17.svg
 
Prove that \(PQ = RS\), if \(PM = MS\), and \(QM = MR\). Also prove that \(M\) is the mid-point of both \(PS\) and \(QR\).
 
In \(\triangle PMQ\) and (\triangle RMS\).
 
\(PM =\)
 
\(QM =\)
 
 \(\angle RMS\) \(=\) \(\angle\)   ()
 
By congruence rule \(\triangle PMQ \cong \triangle RMS\).
 
\(PQ = RS\) ()
 
 
Similarly  \(M\) is the mid-point of both \(PS\) and \(QR\).