# SOLUTION: how can i proof that diagonals bisect each other in a parallelogram

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 Geometry: Parallelograms Solvers Lessons Answers archive Quiz In Depth

 Question 169616: how can i proof that diagonals bisect each other in a parallelogramAnswer by gonzo(654)   (Show Source): You can put this solution on YOUR website!let ABCD be your parallelogram A is bottom left B is top left C is top right D is bottom right. ----- let ABCD lean to the right so that point B is slightly to the right of point A. all you need is a little tilt to show that it's not a rectangle. ----- draw diagonals AC and BD. AC is the long diagonal and BD is the short diagonal. ----- BC congruent to AD (opposite sides of a parallelogram are congruent) ----- note: AC and BD are diagonals of the parallelogram. they are also transversals that intersect two parallel lines (BC and AD). ----- angle ACB congruent to angle CAD (opposite internal angles caused by the intersection of a transversal with two parallel lines are congruent). likewise, angle DBC congruent to angle BDA. ----- you have triangles AED congruent to triangle CEB (ASA) the ASA is formed by: side BC congruent to side AD angle ACB congruent to angle CAD angle DBC congruent to angle BDA. ----- CE is congruent to AE (corresponding parts of congruent triangles are congruent) BE is congruent to DE (same reason). ----- a sketch of the parallelogram can be found at this website: www.geocities.com/gonzo89p look for 169616 parallelogram shouldn't be too hard to find. it's the only one there. -----