Question

In triangle abc , bm and cn are perpendicular from b and c resp. on any line passing through a .if l is midpoint of bc ,show ml =nl

Answer 1

Construction :- Draw OL perpendicular to MN
Now, If a transversal makes equal intercepts on three or more parallel lines, then any other transversal intersecting them will also make equal intercepts.
BM, CN and OL  are perpendicular to MN
Therefore, BM // CN // OL.

Now, BM // CN // OL and BC is the transversal making equal intercepts i.e. BL = LC.
Therefore, transversal MN willl also make equal intercepts.
OM = ON

In triangles LMO and LNO,
OM = ON
<LOM = <LON = 90⁰
OL is common
As both triangles are comgruent, LM =LN (cpct)

Hope that helps !!

Answer 2

see this attachment.................