Question

determine if the two figures are congruent by using transformations. explain your reasoning. (examples 1 and 2) 1.

Explanation:

Step1: Recall congruence by transformation

Two figures are congruent if one can be mapped onto the other by a sequence of rigid - motions (translations, rotations, reflections).

Step2: Analyze possible transformations

First, try to find a translation that aligns one vertex. Suppose we try to translate $\triangle LMN$ so that point $N$ coincides with point $Y$. After translation, we can see that the orientation of the triangles is different. A rotation is needed. But no matter how we rotate $\triangle LMN$ after translation, we cannot make the sides and angles match exactly with $\triangle YZX$.

Step3: Conclusion

Since we cannot map $\triangle LMN$ onto $\triangle YZX$ using only translations, rotations, and reflections (rigid - motions), the two triangles are not congruent.

Answer:

The two figures (triangles $\triangle LMN$ and $\triangle YZX$) are not congruent because there is no sequence of translations, rotations, and reflections that will map one triangle onto the other.