Question

Consider abc and def no shown. based on the definition of congruence in terms of rigid motions, what can be concluded?

1) abc and def are congruent
2) abc and def are similar
3) abc and def are not congruent
4) abc and def are not similar

Answer 1

Based on the definition of congruence in terms of rigid motions, we can concluded 1) ABC and DEF are congruent

Step-by-step explanation:

This is because they can be transformed into each other through a rigid motion. When we consider the definition of congruence in terms of rigid motions, we can conclude that if the figures ABC and DEF can be transformed into each other through a rigid motion (such as translation, rotation, or reflection), then they are congruent.

If two figures are similar, it means that they have the same shape but different sizes. In this case, since we are considering congruence (which requires the figures to have the same size), option 2) ABC and DEF are similar, is not correct.

If the figures ABC and DEF cannot be transformed into each other through rigid motions, then they are not congruent. Therefore, option 3) ABC and DEF are not congruent is not correct.

Similarly, if the figures ABC and DEF do not have the same shape, they are not similar. Thus, option 4) ABC and DEF are not similar, is also not correct. Therefore, the correct answer is 1) ABC and DEF are congruent.