Question

a parallelogram is translated 5 units to the left and reflected across y-axis. which of the following is true about parallelograms?

the two parallelograms are not congruent and a rigid motion was performed.

the two parallelograms are not congruent and a non-rigid motion was performed.

the two parallelograms are congruent and a rigid motion was performed.

the two parallelograms are congruent and a non-rigid motion was performed.

Explanation:

Step1: Recall Rigid Motion Definition

Rigid motions (translations, reflections, rotations) preserve shape and size, so figures remain congruent.

Step2: Analyze Transformations

Translation (5 units left) and reflection (over y - axis) are both rigid motions. These transformations don't change the side lengths or angles of the parallelogram, so the two parallelograms are congruent, and a rigid motion was performed.

Step3: Evaluate Options

• First option: Says not congruent (wrong, rigid motions preserve congruence).
• Second option: Says not congruent and non - rigid (both wrong).
• Third option: Says congruent and rigid motion (matches our analysis).
• Fourth option: Says non - rigid motion (wrong, translation and reflection are rigid).

Answer:

The two parallelograms are congruent and a rigid motion was performed. (The option corresponding to this statement, e.g., if it's the third option in the list, then "The third option: The two parallelograms are congruent and a rigid motion was performed.")