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Show that a median of a triangle divides...

Show that a median of a triangle divides it into two triangles of equal area. GIVEN : A ` A B C` in which `A D` is the median. TO PROVE : `a r( A B D)=a r( A D C)` CONSTRUCTION : Draw `A L_|_B C`

Text Solution

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Proof:
Since `D` is the midpoint of `BC`, we have:
`BD=DC`
Multiplying with 1/2 `AL` on both sides, we get:
`1/2xxBDxxAL=1/2xxDCxxAL`
`ar(triangleABD)=ar(triangleADC)`
Hence Proved.
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