Question

rectangle hjkl is rotated 90° clockwise about the origin to form rectangle hjkl.
which statement is true?
the sum of the angle measures of rectangle hjkl is 180° less than the sum of the angle measures of rectangle hjkl.
the side lengths of rectangle hjkl are twice the corresponding side lengths of rectangle hjkl.
rectangle hjkl is congruent to rectangle hjkl.
the area of rectangle hjkl is \\(\frac{1}{2}\\) the corresponding area of rectangle hjkl.

Explanation:

1. For the first option: The sum of interior angles of any rectangle (a quadrilateral) is \(360^\circ\). Rotation doesn't change the angle measures, so the sum remains \(360^\circ\) for both rectangles. So this statement is false.
2. For the second option: A \(90^\circ\) clockwise rotation about the origin is a rigid transformation. Rigid transformations (like rotation) preserve side lengths. So the side lengths of \(H'J'K'L'\) are equal to those of \(HJKL\), not twice. This statement is false.
3. For the third option: Rotation is a rigid transformation. Rigid transformations preserve the shape and size of a figure, meaning the original figure (rectangle \(HJKL\)) and the image (rectangle \(H'J'K'L'\)) are congruent. This statement is true.
4. For the fourth option: Since rotation is a rigid transformation and side lengths are preserved, the area (which depends on side lengths for a rectangle, \(A = length\times width\)) should be the same for both rectangles. So this statement is false.

Answer:

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