Question

which composition of transformations will create a pair of similar, not congruent triangles?
a rotation, then a reflection
a translation, then a rotation
a reflection, then a translation
a rotation, then a dilation

Explanation:

Step1: Analyze rigid transformations

Rotation, reflection, and translation are rigid transformations. They preserve the shape and size of the figure. So, a rotation - then - reflection, a translation - then - rotation, or a reflection - then - translation will result in congruent triangles.

Step2: Analyze non - rigid transformation

Dilation is a non - rigid transformation. It changes the size of the figure but not the shape. When we first rotate a triangle (a rigid transformation that preserves shape and size) and then dilate it (a non - rigid transformation that changes size), the two triangles will be similar (same shape) but not congruent (different sizes).

Answer:

D. a rotation, then a dilation