Question

are the pockets on this shirt congruent? if so, describe a composition of rigid motions that maps one pocket to the other. choose the correct answer below. a. the pockets on this shirt are congruent. to map the pocket on the left to the pocket on the right, translate the left pocket down and then reflect it across the row of buttons. b. the pockets on this shirt are congruent. to map the pocket on the left to the pocket on the right, rotate it 180° clockwise and then reflect over a vertical line. c. the pockets on this shirt are congruent. to map the pocket on the left to the pocket on the right, reflect it across the row of buttons. d. the pockets on this shirt are not congruent.

Explanation:

Step1: Analyze congruence

Since the shirt pockets are identical in shape and size, they are congruent.

Step2: Analyze option A

Translate the left - pocket down (vertical movement) to align its vertical position with the right - pocket, then reflect across the row of buttons (horizontal symmetry line). This maps the left - pocket to the right - pocket.

Step3: Analyze option B

Rotating \(180^{\circ}\) clockwise and reflecting over a vertical line would not map the left - pocket to the right - pocket as per the shirt's design.

Step4: Analyze option C

Just reflecting across the row of buttons without translation does not account for the vertical mis - alignment of the pockets in the initial position.

Step5: Analyze option D

Since the pockets are identical in shape and size, they are congruent, so this option is wrong.

Answer:

A. The pockets on this shirt are congruent. To map the pocket on the left to the pocket on the right, translate the left pocket down and then reflect it across the row of buttons.