Question

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

Explanation:

Step1: Analyze rigid transformations

Rigid transformations include reflection, rotation, and translation. Dilation is not a rigid transformation as it changes the size.

Step2: Check each option

• Reflection, then rotation: Unlikely as it may not align the triangles properly.
• Reflection, then translation: Unlikely as reflection may not set the right orientation.
• Rotation, then translation: Rotate \(\triangle FGH\) to match the orientation of \(\triangle VWX\) and then translate to map it exactly.
• Rotation, then dilation: Dilation is not rigid, so this is incorrect.

Answer:

rotation, then translation