Question

the triangles are congruent by sss or hl. the diagram shows the sequence of three rigid transformations used to map △abc onto △abc. what is the sequence of the transformations? ∘ rotation, then reflection, then translation ∘ rotation, then translation, then reflection ∘ reflection, then translation, then rotation ∘ reflection, then rotation, then translation

Explanation:

1. First, analyze the reflection: Reflecting \(\triangle ABC\) over the line (e.g., the perpendicular bisector or a vertical/horizontal line) to get a triangle with a mirrored orientation, which is a common first step in such transformations.
2. Then, rotation: After reflection, rotating the triangle around a point (like a vertex or the origin) to align it more closely with \(\triangle A''B''C''\)'s orientation.
3. Finally, translation: Moving (translating) the rotated triangle to the exact position of \(\triangle A''B''C''\) since translation is a slide without rotation or reflection.

Checking the options, the sequence of reflection, then rotation, then translation matches the logical order of transforming \(\triangle ABC\) to \(\triangle A''B''C''\) through rigid motions.

Answer:

D. reflection, then rotation, then translation