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:

A rotation is a rigid transformation that preserves shape and size. A reflection is a rigid transformation that preserves shape and size. A translation is a rigid transformation that preserves shape and size. A dilation is a non - rigid transformation that changes the size of a figure but not its shape. Similar triangles have the same shape (corresponding angles are equal) but not necessarily the same size. Congruent triangles have the same shape and size.

• For a rotation then a reflection: Both are rigid transformations. The resulting triangle will be congruent to the original triangle.
• For a translation then a rotation: Both are rigid transformations. The resulting triangle will be congruent to the original triangle.
• For a reflection then a translation: Both are rigid transformations. The resulting triangle will be congruent to the original triangle.
• For a rotation then a dilation: Rotation (rigid transformation) preserves shape and size, dilation (non - rigid transformation) changes the size. The resulting triangle will be similar (same shape) but not congruent (different size) to the original triangle.

Answer:

a rotation, then a dilation