SOLUTION: Given triangle ABC , perpendicular BED , line AB equal and congruent to line CB and D is the midpoint of line AC. Prove line AE equal and congruent to line CE.

Algebra ->  Geometry-proofs -> SOLUTION: Given triangle ABC , perpendicular BED , line AB equal and congruent to line CB and D is the midpoint of line AC. Prove line AE equal and congruent to line CE.      Log On


   

Question 1029464: Given triangle ABC , perpendicular BED , line AB equal and congruent to line CB and D is the midpoint of line AC. Prove line AE equal and congruent to line CE.
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Since D is the midpoint of of AC, AD = DC
Since BED is a perpendicular, angle ADB and angle CDB are each right angles
By SAS, Side Angle Side, we know triangle ADE is congruent to triangle CDE,
where AD = DC, angle ADB = CDB and DE = DE since the lines are coincident.
Since the triangles are congruent, AE = EC