Question

Alon was curious if segments \overline{JK} JK start overline, J, K, end overline and \overline{NM} NM start overline, N, M, end overline were congruent, so he tried to map one figure onto the other using transformations: Alon concluded: "It's not possible to map \overline{JK} JK start overline, J, K, end overline onto \overline{NM} NM start overline, N, M, end overline using a sequence of rigid transformations, so the segments are not congruent." What error did Alon make in his conclusion?

Answer 1

Explanation:

It would be A - One more transformation - a rotation - would map JK onto NM. So the segments are congruent.

Let's see if a sequence of JK start overline, J, K, end overline onto

NM start overline, N, M, end overline. If it is possible, then the segments are congruent.

There are many possible sequences of transformations that may map one figure onto another.

Alon translated point J onto point N.

Is there another rigid transformation we could now use to complete the mapping?

Let's try rotating 90° about point N.

Alon concluded, "It's not possible to map JK start overline, J, K, end overline onto NM using a sequence of rigid transformations, so the segments are not congruent," but he made an error.

One more transformation — a rotation — would map JK onto NM. So the segments are congruent.

Answer 2

The answer is A because Alon could have rotated the figure and discovered that they are congruent