Question

which of the following sequences of transformations, when applied to a parallelogram, will produce a parallelogram with the same side lengths and angle measures? select all the correct answers. a translation followed by a dilation a dilation followed by a reflection a rotation followed by a reflection a reflection followed by a translation

Explanation:

Step1: Understand rigid - motions

Rigid - motions (isometries) preserve side lengths and angle measures. Rotations, reflections, and translations are rigid - motions.

Step2: Analyze dilation

Dilation changes the size of a figure. A dilation with a scale factor other than 1 will change the side lengths of the parallelogram. So sequences with dilation do not preserve side lengths and angle measures.

Step3: Analyze rotation - reflection

A rotation followed by a reflection is a composition of two rigid - motions. It will preserve side lengths and angle measures.

Step4: Analyze reflection - translation

A reflection followed by a translation is a composition of two rigid - motions. It will preserve side lengths and angle measures.

Answer:

C. a rotation followed by a reflection
D. a reflection followed by a translation