Question

triangle def is similar to triangle def
which similarity transformation could map △def to △def?
o dilation and reflection
o dilation and translation
o rotation and dilation
o rotation and reflection

Explanation:

Step1: Analyze dilation

Similar triangles can be obtained by dilation (scaling). Since \(\triangle DEF\) and \(\triangle D'E'F'\) are similar, dilation (changing the size proportionally) is involved.

Step2: Analyze rotation

The orientation of \(\triangle D'E'F'\) is different from \(\triangle DEF\). Rotation (turning around a point) changes the orientation of a figure. A reflection would flip the figure over a line (which is not the case here as there is no mirror - like flip in the general sense of the orientation change shown), and a translation would just slide the figure without rotation or resizing. So, rotation (to change orientation) and dilation (to change size while keeping similarity) are the transformations.

Answer:

C. rotation and dilation