SOLUTION: Given: Triangle ABC where AB is not congruent to BC, BD is a median. Prove: BD is not perpendicular to AC.

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Question 253026: Given: Triangle ABC where AB is not congruent to BC, BD is a median.
Prove: BD is not perpendicular to AC.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!

First thing is to draw the figures.
We have a triangle ABC where AB does not equal BC.
BD is the median splitting AC in two equal parts
If BD were perpendicular to AC then angle BDC and angle BDA would be right angles.
If they were right angles then BD^2+CD^2 would equal BC^2
and AD^2+BD^2 would equal AB^2
and since BD=BD and AD=DC then BC and BA would be equal but we are told that AB is not congruent to BC therefore they can't be right triangles and therefore angle BDC and angle BDA are not right angles.
Since they are not right angles, the lines(segment) BD and AC are not perpendicular. QED.