Question

In the figure given below $AD$ is a median and $BL$, $CM$ are pendicular drawn from $B$ and $C$ respectively on $AD$ and $AD$ produced to $M$. Then $BL=CM$

• A. True
• B. False

Answer 1

The correct option is A True

$BL\perp AD$ and $DM\perp CM$ [ Given ]

In $△BLD$ and $△CMD,$

$\Rightarrow$ $\angle BLD=\angle CMD={90}^o$ [ Given ]

$\Rightarrow$ $\angle BLD=\angle MDC$ [ Vertically opposite angles ]

$\Rightarrow$ $BD=DC$ [ Since, $AD$ is median to $BC$ ]

$\therefore$ $△BLD\cong △CMD$ [ By $AAS$ congruence rule ]

We know that, corresponding parts of the congruent triangles are equal.

$\therefore$ $BL=CM$