Question

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

Explanation:

Step1: Understand rigid transformations

Rigid transformations include reflection, rotation, and translation. Dilation is not a rigid transformation as it changes the size of the figure. Since the triangles are congruent (same size and shape), we can rule out the option with dilation.

Step2: Analyze rotation and translation

If we rotate \(\triangle ADC\) (assuming \(ABC\) is a typo and it's \(ADC\)) around a point (for example, the mid - point of \(CD\) and \(DE\) after some orientation analysis) and then translate it (move it without rotating or reflecting again), we can map \(\triangle ADC\) onto \(\triangle FED\).

• Reflection then translation: If we reflect \(\triangle ADC\) over a line, the orientation of the right - angle (for example, if we assume the right - angle in \(\triangle ADC\) at \(D\) and in \(\triangle FED\) at \(E\)) would not match easily with just a reflection and then a translation.
• Rotation then reflection: Rotation and then reflection would change the orientation in a non - matching way for these two congruent right - angled triangles (with the given side lengths \(12\), \(16\), \(20\)) to map exactly.

Answer:

rotation, then translation