BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. If L is the mid-point of BC, prove that LM=LN.

Question

Philoid · Accepted Answer

draw LS perpendicular to line MN

∴ the line BM , LS,CN being the same perpendiculars , on line MN are parallel to each other

We have , BL=LC (L is mid point of BC)

Using intercept theorem,

MS = SN………………(i)

Now in ∆MLS and ∆LSN

MS=SN

∠LSM=∠LSN = 90° ( LS perpendicular to MN) and SL=LS is common

∴∆MLS ≅∆LSN (SAS congruency )

∴ LM= LN proved