Question

State true or false:

In triangle $ABC$, the medians $BP$ and $CQ$ are produced upto points $M$ and $N$ respectively such that $BP=PM$ and $CQ=QN$. Hence, $M,A$ and $N$ are not collinear.

• A. True
• B. False

Answer 1

The correct option is B False

Given: $BP$ and $CQ$ are medians of $AB$ and $AC$ respectively of triangle $ABC$
$BP$ and $CQ$ are produced to $M$ and $N$ such that $BP=PM$ and $CQ=QN$
In $△APM$ and $△BPC$,
$AP=PC$
$PM=BP$
$\angle APM=\angle BPC$ (Vertically opposite angles)
therefore, $△APM\cong △BPC$ (SAS rule)
$\angle AMP=\angle BCP$ (By cpct)
Similarly, $△AQN\cong △BPC$
hence, $\angle ANQ=\angle QBC$ (By cpct)
Hence, $N,A,M$ lie on a straight line.