Answer :
Final answer:
The statement that Pentagon ABCD is congruent to Pentagon ABCDE is true when Pentagon ABCDE is rotated 180 degrees about the origin. This is because a 180-degree rotation does not change the size or shape of the figure, only its position or orientation.
Explanation:
The correct statement regarding a 180-degree rotation of Pentagon ABCDE about the origin to form Pentagon ABCD is that Pentagon ABCD is congruent to Pentagon ABCDE (option a). This is because a 180-degree rotation of a figure about the origin does not change the shape or size of the figure, it only changes its position or orientation in the coordinate plane. You can visualize it imagining flipping the pentagon over once, like flipping a pancake. The top-side becomes the bottom-side, but the shape and size of the pentagon remain the same.
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Final answer:
A rotation in geometry is a form of transformation where a figure turns about a fixed point called the center of rotation. If a Pentagon ABCD is rotated 180 degrees clockwise, it forms another Pentagon ABCDE. The rotation doesn't change the shape or size of the original pentagon ABCD, hence, it is congruent to the Pentagon ABCDE.
Explanation:
The term rotation in geometry is a transformation that turns a figure about a fixed point called the center of rotation. The degree of rotation measures the amount that a figure is turned counterclockwise about a point. If the pentagon ABCD is rotated 180 degrees clockwise about the origin, it creates another pentagon, ABCDE. Since a rotation doesn't change the shape or size of the figure, only its orientation or direction, the original pentagon ABCD is congruent to the new Pentagon ABCDE. Meaning, they have the same shape and size but different orientations.
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