Question

triangle def is congruent to δ ghj by the sss theorem. which rigid transformation is required to map δ def onto δ ghj?
options:

• dilation
• reflection
• rotation
• translation

Explanation:

1. First, recall the definitions of rigid transformations:

• Dilation is not a rigid transformation as it changes the size (scales the figure), so we can eliminate dilation.
• Reflection flips a figure over a line. Looking at the triangles, their orientation doesn't suggest a flip is needed.
• Rotation turns a figure around a point. The triangles don't seem to require a rotation to align.
• Translation is a slide (moving the figure without rotating or reflecting) that preserves the shape and size. The triangles $\triangle DEF$ and $\triangle GHJ$ appear to be in positions where a translation (sliding) would map one onto the other since their orientation and shape are the same, just shifted.

Answer:

D. translation