John has written the following proof showing that the diagonals of a parallelogram are equal in length. The diagonals of a parallelogram are not necessarily equal, so he must have made an error. Identify and explain the error.
3 years ago
Answered By Emily D
You're missing part of this question, but it looks like a similar one was asked a few years ago so I'll try to answer using that version!
INCORRECT PROOF:
AB = ED | Opposite sides of parallelogram
BAE = AED | Alternate interior angles****
ABD = BDE | Alternate interoir angles****
ABC = EDC | ASA
BC = EC | Corresponding sides of congruent angles
AC = DC | Corresponding sides of congruent angles
AE = BD | AC + CE = DC + CB
WHY IT'S INCORRECT:
This is easier to understand if you draw out a diagram of the problem (that funky looking letter should be an E).
****The only way that both BAE = AED and ABD = BDE is if the corners are 90. This would make it a rectangle or square, so still a parallelogram, but parallelograms don't NEED to be squares/rectangles.
3 years ago
Answered By Emily D
You're missing part of this question, but it looks like a similar one was asked a few years ago so I'll try to answer using that version!
INCORRECT PROOF:
AB = ED | Opposite sides of parallelogram
BAE = AED | Alternate interior angles****
ABD = BDE | Alternate interoir angles****
ABC = EDC | ASA
BC = EC | Corresponding sides of congruent angles
AC = DC | Corresponding sides of congruent angles
AE = BD | AC + CE = DC + CB
WHY IT'S INCORRECT:
This is easier to understand if you draw out a diagram of the problem (that funky looking letter should be an E).
****The only way that both BAE = AED and ABD = BDE is if the corners are 90. This would make it a rectangle or square, so still a parallelogram, but parallelograms don't NEED to be squares/rectangles.
Attached Whiteboard:
Play Drawing