# SOLUTION: how do i prove if the diagnols of a parallelogram are congruent the parallelgram is a rectangle

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 Question 233169: how do i prove if the diagnols of a parallelogram are congruent the parallelgram is a rectangleAnswer by Theo(3464)   (Show Source): You can put this solution on YOUR website!If it is a parallelogram, then the opposite sides are equal. If the diagonals are also equal, then you have 4 congruent triangles. Let your parallelogram be ABCD where: A is top left corner. B is top right corner. C is bottom right corner. D is bottom left corner. Opposite sides are: AB and CD AD and BC Diagonals are: AC BD Triangles that are congruent are: ADC with CBA by SSS because: AD = BC AC = AC AB = DC This means that angle ADC = angle ABC because congruent angles of congruent triangles are congruent. BCD with DAB by SSS because: AD = BC DC = AB BD = BD This means that angle DAB equals angle BCD because congruent angles of congruent triangles are congruent. Since the opposite angles of a parallelogram are supplementary (sum of their angles is equal to 180 degrees), this means that: angle ADC = 90 degrees angle ABC = 90 degrees angle DAB = 90 degrees angle BCD = 90 degrees This means that parallelogram ABCD is a rectangle because a rectangle is a parallelogram with all angles being 90 degrees.