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

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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.

  


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