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if C is midpoint of AB and D is the midpoint of AC. Prove that AD =1/4 AB.

               
Given C is the midpoint of AB and D is the midpoint of AC.
therefore, AB = AC + BC
Ac = BC [since C is the midpoint of AB]
therefore AB = AC + AC
ie., AB = 2AC        ............(1)
Also, AC = AD + CD
AD = CD [since D is the midpoint of AC]
therefore AC = AD + AD
AC = 2AD             ..............(2)
Substituting (2) in (1)
AB = 2AC
     = 2[2AD]
AB = 4AD
ie., AD = 1/4AB
Hence proved.


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