SOLUTION: Is parallelogram ABCD shown in the image a rectangle? Here is a link to the image: https://imgur.com/a/vZUwspf (I got this answer wrong, but I'm not really sure why. This was my

Algebra ->  Parallelograms -> SOLUTION: Is parallelogram ABCD shown in the image a rectangle? Here is a link to the image: https://imgur.com/a/vZUwspf (I got this answer wrong, but I'm not really sure why. This was my       Log On


   

Question 1183621: Is parallelogram ABCD shown in the image a rectangle? Here is a link to the image: https://imgur.com/a/vZUwspf (I got this answer wrong, but I'm not really sure why. This was my exact answer: Yes, parallelogram ABCD is a rectangle because the diagonals are shown to have equal length.)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
proof:
Given above is parallelogram ABCD and we want to prove the diagonals bisects each other into equal lengths.
First we join the diagonals and where they intersect is point E.
Angle ECD and EAB+are equal (given), then lines CD and AB are parallel and that makes them alternate angles.
Angles EDC and EBA are equal in measure for the same reason.
Line CD and AB are equal in length because opposite sides in a parallelogram are are equal.
Therefore triangle ABE and CED are congruent because they have 2 angles and a side in common.
Hence line CE and EB are equal and AE and ED are equal due to congruent triangles.
Therefore the diagonals of a parallelogram do bisect each other into equal parts.
since
DE%2BEB+=DB
AE%2BEC=AC
=> diagonals AC=DB
So, a parallelogram ABCD shown in the image is a rectangle.