Question

In the given figure, two sides $AB$ and $BC$ and the median $AD$ drawn to side $BC$ of $△ABC$ are equal to the two sides $PQ$ and $QR$ and the corresponding median $PM$ of the other $△PQR.$ Which of the following is not correct$?$

• A. $△ABD\cong △PQM$
• B. $△ABC\cong △PQR$
• C. $△ABD\cong △PMR$
• D. $△ADC\cong △PMR$

Answer 1

Answer: (C)

In $△$s $ABD$ and $PQM$
$AB=PQ$
$AD=PM$ (Given)
$BD\left(\frac{1}{2}BC\right)=QM\left(\frac{1}{2}QR\right)$
$\therefore$ $△ABD\cong △PQM$ (SSS)
$\angle B=\angle Q$ (cpct)
In $△$s $ABC$ and $PQR$
$AB=PQ$ (Given)
$\angle B=\angle Q$ (Prove above)
$BC=QR$ (Given)
$\therefore$ $△ABC\cong △PQR$ (SAS)
$AC=PR$ (cpct)
In $△$s $ADC$ AND $PMR$
$AD=PM$ (Given)
$DC\left(\frac{1}{2}BC\right)=MR\left(\frac{1}{2}QR\right)$ (Given)
$AC=PR$ (Prove above)
$\therefore$ $△ADC\cong △PMR$ (SSS)
$\therefore$ $△ABD≆△PMR$