Question

triangle def is congruent to △ghj by the sss theorem. which rigid transformation is required to map △def onto △ghj? dilation reflection rotation translation

Explanation:

Step1: Recall rigid transformation properties

Rigid transformations (reflection, rotation, translation) preserve shape and size. Dilation is not a rigid transformation as it changes size. Since \(\triangle DEF\cong\triangle GHJ\) (same - size), dilation is out.

Step2: Analyze orientation

Translation moves a figure without rotation or reflection. If we look at the orientation of the triangles: \(\triangle DEF\) and \(\triangle GHJ\) have the same - side markings (congruent sides), but the order of vertices (if we consider the base) is such that a reflection (a flip over a line) is not needed. A rotation (turning around a point) is also not the case.

Step3: Check translation

Translation slides a figure. We can think of moving \(\triangle DEF\) (without rotating or reflecting) to map it onto \(\triangle GHJ\) since the side - length relationships (from SSS) and the general shape (congruent) can be achieved by just shifting the position of \(\triangle DEF\) in the plane.

Answer:

translation