In a ` A B C ,\ B M\ a n d\ C N` are perpendiculars from `B\ a n d\ C` respectively on any line passing through `Adot` If `L` is the mid-point of `B C` , prove that `M L=N L`.

Explanation

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` parallel to `CN` parallel to `OL`.
Now, `BM` parallel to `CN` parallel to `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`
`angleLOM=angleLON=90^@`
`OL` is common
As both triangles are congruent.
`therefore LM =LN (CPCT)`
Hence Proved.