SOLUTION: Given: DB is perpendicular to AC, B is the midpoint of AC. Prove: DA is congruent to DC

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Question 247498: Given: DB is perpendicular to AC, B is the midpoint of AC.
Prove: DA is congruent to DC
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
I haven't tried geometry proofs in awhile.
so here goes.
we have two right triangles
dbc and dba
we know that they are right triangles because db is perpendicualr to ac
we know that db=db
we also know that ba=bc since b is the midpoint of ac
we also know that angle dba is right angle as well as angle dbc
so we have a right triangle with two legs that are equal therefore the hypotenuses are congruent since a^2+b^2=c^2 and we have the same legs (a and b) in both right triangles