Question

the triangles are congruent by the sss congruence theorem. which rigid transformation(s) can map $\triangle fgh$ onto $\triangle vwx$?

• reflection, then rotation
• reflection, then translation
• rotation, then translation
• rotation, then dilation

Explanation:

1. First, recall that rigid transformations preserve the shape and size of the figure (reflection, rotation, translation are rigid; dilation is non - rigid, so eliminate the option with dilation).
2. Analyze the positions of $\triangle FGH$ and $\triangle VWX$. If we first reflect $\triangle FGH$ over a line (to align the corresponding sides and angles in a mirrored way) and then translate (slide) it, we can map $\triangle FGH$ onto $\triangle VWX$. Rotation followed by translation or reflection followed by rotation do not align the triangles as appropriately as reflection then translation in this case.

Answer:

B. reflection, then translation