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: Recall transformation properties

Rotations, reflections, translations are rigid transformations (preserve size and shape, so congruent). Dilation changes size (scales), so affects congruence but preserves similarity (same shape, different size).

Step2: Analyze each option

• Rotation + Reflection: Both rigid, result congruent (and similar).
• Translation + Rotation: Both rigid, result congruent (and similar).
• Reflection + Translation: Both rigid, result congruent (and similar).
• Rotation + Dilation: Rotation (rigid, preserves shape/size), then dilation (changes size, so triangles are similar (same shape) but not congruent (different size)).

Answer:

D. a rotation, then a dilation