Question

the triangles are congruent by the sss congruence theorem. which rigid transformation(s) can map △abc onto △dec? 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 the orientation and position don't match this sequence.
• Reflection, then translation: Unlikely as the orientation and position don't match this sequence.
• Rotation, then translation: First, rotate \(\triangle ABC\) around point \(C\) to align the sides, then translate it to map onto \(\triangle DEC\).
• Rotation, then dilation: Dilation is not a rigid transformation.

Answer:

rotation, then translation