Question 233169: how do i prove
if the diagnols of a parallelogram are congruent the parallelgram is a rectangle Answer by Theo(13342) (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.
to show you what i mean, let the parallelogram be PQRS.
you have:
PQ = SR
PS = QR
PR = SQ
you can break your parallelogram into 4 triangles.
those triangles are:
PRS and RPQ
SPQ and QRS
all these triangles are congruent by SSS as shown in the following diagram.
since all these triangles are congruent, then all their corresponding angles are congruent.
this means that angle PSR is congruent to angle RQP is congruent to angle SPQ is congruent to angle QRS.
this means that all 4 angles of the parallelogram are congruent to each other.
this means that all the angles of the parallelogram are equal to 90 degrees.
since all the angles of a rectangle are equal to each other, this means that the parallelogram is a rectangle.
it hss all 4 angles equal to each other.
it has both diagonals equal to each other.
that's all that you need because that's what defines a rectangle.
