Question

two triangles are shown.
what transformations can be used to show that $\triangle lmn$ is similar to $\triangle pqr$?

Explanation:

Similarity between triangles can be shown via transformations that preserve shape but not size, and can include orientation changes. First, a dilation (reduction) of $\triangle LMN$ by a scale factor less than 1 will shrink it to the size of $\triangle PQR$. Then, a rotation (to match the triangular orientation) and/or translation (to move the shrunk triangle to the position of $\triangle PQR$) will align the two triangles, proving they are similar.

Answer:

A dilation (reduction) of $\triangle LMN$ to the size of $\triangle PQR$, followed by a rotation and translation to align the two triangles, can be used to show their similarity.