Question

the triangles are congruent by sss.
which transformation(s) can be used to map one triangle onto the other? select two options.
□ reflection only
□ translation only
□ dilation, then translation
□ rotation, then translation
□ rotation then dilation

Explanation:

Step1: Recall Congruent Transformations

Congruent transformations (isometries) preserve shape and size: reflection, rotation, translation. Dilation changes size, so options with dilation are invalid (triangles are congruent, so no dilation).

Step2: Analyze the Triangle Orientation

The triangles have a symmetric orientation (right angle, congruent sides). Reflection over a vertical/horizontal line can map one to the other. Also, rotation (e.g., 180°) followed by translation can align them. Translation alone won't work as orientation differs. Reflection only is possible, and rotation then translation is also possible (since rotation can adjust orientation, then translation to position).

Step3: Eliminate Invalid Options

• Dilation options: Invalid (congruent, no size change).
• Translation only: Orientation mismatch, so no.
• Reflection only: Valid (mirror image).
• Rotation, then translation: Valid (rotate to align, then translate).

Answer:

reflection only, rotation, then translation