Question

In the given figure, AD is the median and AD is produced to M. BL and CM are perpendiculars drawn from B and C respectively on AM.



Which of these is true?

• A. BL = CD
• B. CM = AB
• C. BL= CM
• D. MD = BL

Answer 1

The correct option is C BL= CM



In $\Delta BLD$ and $\Delta CMD$
BD = CD
(AD is median on BC)
$\angle BLD=\angle CMD={90}^0$
$(BL\perp AM,CM\perp AM)$
$\angle BDL=\angle CDM$Vertically opposite angles)
$\Delta BLD\cong \Delta CMD$ (by AAS congruence criterion)
$\Rightarrow BL=CM$ (CPCT)

So, option c is correct.