SOLUTION: In Triangle ABC, AD is a median. Prove that AB^2 + AC^2 = 2AD^2 + 2DC^2.

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Question 208755: In Triangle ABC, AD is a median.
Prove that AB^2 + AC^2 = 2AD^2 + 2DC^2.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
In Triangle ABC, AD is a median.
Prove that AB^2 + AC^2 = 2AD^2 + 2DC^2.



AB%5E2=BD%5E2%2BAD%5E2 by the Pythagorean theorem

AC%5E2=DC%5E2%2BAD%5E2 by the Pythagorean theorem

AB%5E2%2BAC%5E2=BD%5E2%2BDC%5E2+%2B+2AD%5E2 because equals 
                 added to equals 
                 give equals.

BD=DC because Median AD bisects side BC

AB%5E2%2BAC%5E2=DC%5E2%2BDC%5E2+%2B+2AD%5E2  Substituting DC for BD

AB%5E2%2BAC%5E2=2DC%5E2%2B+2AD%5E2   Combining like terms.

Edwin