Question

the triangles are congruent by the sss congruence theorem. which rigid transformation(s) can map δfgh onto δvwx? reflection, then rotation reflection, then translation rotation, then translation rotation, then dilation

Explanation:

Step1: Analyze Rigid Transformations

Rigid transformations (reflection, rotation, translation) preserve congruence (shape and size). Dilation changes size, so options with dilation (rotation, then dilation) are invalid. Now, check reflection/rotation + translation.

Step2: Check Triangle Orientation

First, reflect \( \triangle FGH \) over the vertical line (to align the sides), then translate (slide) to match \( \triangle VWX \). Rotation alone or reflection + rotation may not align as well. The correct sequence is reflection, then translation (since after reflection, a translation can move the triangle to the correct position, and both are rigid transformations preserving congruence). The option "reflection, then translation" fits.

Answer:

The option "reflection, then translation" (the second option among the choices, with text "reflection, then translation").