## Alberta Free Tutoring And Homework Help For Math 20-2

0

Help

### 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 parallelogramBAE = AED   |      Alternate interior anglesABD = BDE   |     Alternate interoir anglesABC = EDC   |   ASABC = EC      |   Corresponding sides of congruent anglesAC = DC      |   Corresponding sides of congruent anglesAE = BD      |   AC + CE = DC + CB

3 years ago

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.