SOLUTION: Given: CD bisects AB CD perpendicular to AB Prove: CA is congruent to CB

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Question 834288: Given: CD bisects AB
CD perpendicular to AB
Prove: CA is congruent to CB
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Since cd is perpendicular to AB we have two right triangles
cad and cbd
Since cd bisects ab then ad =db
we have
ad^2+cd^2=ca^2
and
db^2+cd^2=cb^2
but since
ad=db then
ad^2=db^2
therefore
ad^2+cd^2=db^2+cd^2
hence
ca^2=cb^2
therefore
ca=cb
QED