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,

$A$ is the mid-point of $MN$.

• A. True
• B. False

Answer 1

The correct option is A True

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)
$\angle AMP=\angle BPC$ (By cpct)
Similarly, $△AQN\cong △BPC$
hence, $\angle ANQ=\angle BCQ$ (By cpct)
Hence, N, A, M lie on a straight line.
$NM=NA+AM=BC+BC=2BC$
hence, A is the mid point of MN