In a triangle ABC, AD is a median. Whether 2AD>AB+AC.
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no it is not
AB + AC > 2 AD
Construct a parallelogram from ΔABC by drawing CE parallel to AB and BE parallel to AC. Now extend AD to join E. AE is the diagonal and we know in a parallelogram the diagonals bisect each other.
Since AEC is a triangle, sum of two sides is more than the third side
AC + CE > AE, CE = AB and AE = 2 AD
AC + AB > 2 AD
hence the result
AB + AC > 2 AD
Construct a parallelogram from ΔABC by drawing CE parallel to AB and BE parallel to AC. Now extend AD to join E. AE is the diagonal and we know in a parallelogram the diagonals bisect each other.
Since AEC is a triangle, sum of two sides is more than the third side
AC + CE > AE, CE = AB and AE = 2 AD
AC + AB > 2 AD
hence the result
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