Question

rectangle hjkl is rotated 180° clockwise about the origin to form rectangle hjkl. which statement is true? rectangle hjkl is congruent to rectangle hjkl. the side lengths of rectangle hjkl are twice the corresponding side lengths of rectangle hjkl. the sum of the angle measures of rectangle hjkl is 180° less than the sum of the angle measures of rectangle hjkl. the area of rectangle hjkl is 2 times the corresponding area of rectangle hjkl.

Explanation:

• A \(180^\circ\) rotation about the origin is a rigid transformation. Rigid transformations (like rotations, translations, reflections) preserve the shape and size of a figure, meaning the pre - image (rectangle \(HJKL\)) and the image (rectangle \(H'J'K'L'\)) are congruent.
• For the second option, since it's a rigid transformation, side lengths do not double.
• For the third option, the sum of the interior angles of a rectangle is always \(360^\circ\) (since a rectangle has four right angles, \(4\times90^\circ = 360^\circ\)), so the sum of angles will not change.
• For the fourth option, since the rectangles are congruent (same side lengths), the area of \(H'J'K'L'\) will be equal to the area of \(HJKL\), not twice.

Answer:

A. Rectangle \(HJKL\) is congruent to rectangle \(H'J'K'L'\).