In a triangle ABC in which L is the mid point of BC and M is the mid point of AL prove that area AMC=1/4 area ABC
Answer
Text Version of the Answer is
In ∆ABC,
AL is median and cuts a triangle into two equal parts/Area
∴ ar ∆ALC = ar ALB
We know,
ar ∆ABC = ar ∆ALC + ar ∆ALB
= ar ∆ALC + ar ∆ALC
→ 1/2 ar ∆ABC = ∆ALC ….(1)
In ∆ ALC, MC is a median
∴ a ∆AMC = Ar ∆MLC
We know,
Ar ∆ ALC = ar ∆ AMC + ar ∆MLC
1/2 ar ∆ABC = ar ∆ AMC + ar ∆AMC
(From (1))
1/2 ar ∆ ABC = 2 ar ∆ AMC
1/4 ar ∆ABC = 2 ar ∆ AMC
Hence proved.
