Troy has written a proof showing that the diagonals of a parallelogram are equal in length. The diagonals of a parallelogram are not necessarily equal so Troy must have made an error. Identify and explain his error.
Statement | Justification
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
6 years ago
Answered By Emily H
To figure out this problem, you will want to draw a diagram so that you can get a better idea of what the problem's asking.
Then, I would relable all the three letter angles as follows just for ease of following which is which:
$EAB=\angle A$EAB=∠A ; $AED=\angle E$AED=∠E ; $BDE=\angle D$BDE=∠D ; $ABD=\angle B$ABD=∠B ; $ABC=\angle B_1$ABC=∠B1 ; $EDC=\angle D_2$EDC=∠D2
So, then looking at the statements, we can see the first is true by definition, no matter the values of the angles.
The second and third statements, when rewritten become $\angle A=\angle E$∠A=∠E and $\angle B=\angle D$∠B=∠D . However, from the diagram we can see that these statements are not necessarily true, except when $\angle A=\angle B=\angle D=\angle E=90$∠A=∠B=∠D=∠E=90, which would indicate a rectangle rather than a more general parallelogram.
As the remainder of this proof requires these two statements to hold, it swiftly falls apart except in the special case.
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