16. )n AABC, AD is the median. If E is any point on AD, then (1) ar(ABE) = ar(ACE) (2) BE = CE (3) AB + BE = AC + CE (4) AE = (BE + CE)/2
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Step-by-step explanation:
ABC is the triangle and O the centroid. Let AO produced meet BC in D. The Area of the triangles ABD = Area of triangle ACD.
(Reason CD=BD and same altitude and Area = 21×base×altitude)
Similarly, Area EBD = Area ECD. Subtracting i.e
Area ABD - Area EBD = Area ACD - Area ECD which implies Area ABE = Area ACE
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