In triangle ABC, if L and M are the points on AB AC respectively, such that LM is - Maths - Areas of Parallelograms and Triangles

Question

In triangle ABC, if L and M are the points on AB & AC
respectively, such that LM is parallel to BC If BM & CL
intersect at O, prove that area of traingle LOB = area of triangle
MOC

Gopal Mohanty · Accepted Answer

Hi!
<img alt="" height="127" src=
"https://s3mn%20mnimgs%20com/img/shared/userimages/mn_images/image/Tr2%20png"
width="260">
We have LM||BC
ΔBLC and ΔCMB are on
same base BC and have the same height as LM||BC
Therefore ar(ΔBLC) = ar
(ΔCMB)
⇒ ar(ΔLOB) +
ar(ΔBOC) = ar(ΔMOC) + ar
(ΔBOC)
⇒ ar(ΔLOB) =
ar(ΔMOC)
Cheers!

In triangle ABC, if L and M are the points on AB & AC respectively, such that LM is parallel to BC. If BM & CL intersect at O, prove that area of traingle LOB = area of triangle MOC.