The error in Troy's proof lies in statement 4. He states that triangle ABC is approximately equal to triangle EDC using the ASA (Angle-Side-Angle) congruence postulate. However, Troy should have used the SAS (Side-Angle-Side) congruence postulate instead.
Therefore, statement 4 is incorrect, and consequently, statement 5, which claims that BC equals EC based on the congruence of the triangles, is also incorrect. Since the proof relies on these incorrect statements, the final statement is also incorrect.
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 his error(s).
Statement Reason Correct/Incorrect?
A B equals E D Opposite sides of parallelogram blank
angle B A E equals angle A E D Alternate interior angles blank
angle A B D equals angle B D E Alternate interior angles blank
triangle A B C approximately equal to triangle E D C ASA blank
B C equals E C Corresponding sides of congruent triangles blank
A C equals D C Corresponding sides of congruent triangles blank
A E equals B D
A C plus C E equals D C plus C B blank
correct, incorrect, true but based on incorrect statements
1 answer
1 answer