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

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) (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 and we want to prove the diagonals bisects each other into equal lengths.
First we join the diagonals and where they intersect is point .
Angle and are equal (), then lines and are parallel and that makes them alternate angles.
Angles and are equal in measure for the same reason.
Line and are equal in length because opposite sides in a parallelogram are are equal.
Therefore triangle and are congruent because they have 2 angles and a side in common.
Hence line and are equal and and are equal due to congruent triangles.
Therefore the diagonals of a parallelogram do bisect each other into equal parts.
since

=> diagonals
So, a parallelogram shown in the image a .

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