Question

pls solve this fellow sum the line which i draw is divided symbol

Answer 1

In ∆ABC & ∆DBC,
Angle ALO = Angle DMO (each is 90°)
Angle AOL = Angle DOM (vertically opposite angles)

Therefore, ∆ABC~∆DBC (AA test)
so, AL/DM = AO/DO. (i)

ar(∆ABC) = ½ALxBC
ar(∆DBC) = ½DMxBC

Dividing both we get,
ar(∆ABC)/ar(∆DBC) = ½(AL)(BC)/½(DM)(BC)

ar(∆ABC)/ar(∆DBC) = AL/DM

ar(∆ABC)/ar(∆DBC) = AO/DO (from i)

$Hence, proved.$