Question

ABCD IS IIgm .L and M are point on AB AND DC andAL=CM. prove that LM and BD bisect each other

Answer 1

Let BD intersect LM at O
In IIgram ABCD
We have , AL = CM - (i)
And as we know that opp. sides of IIgram are equal , therefore AB =DC -(ii)
Now subtracting equation i from ii
AB -AL = DC- CM
BL = DM
Now, in triangle BOL and triangle DOM
BL =DM (Proved above)
angle BOL = angle DOM ( Vertically opposite angle)
angle OBL =angle ODM ( Alternate interior angle)
therefore ∆ BOL ≈∆DOM
therefore BO= DO , LO =MO ( By c.p.c.t.)