Based on your description of the construction involving segment AB and point C with an arc creating point D, it seems that the construction demonstrates a method for copying a segment accurately by hand.
Here's how the construction is carried out and why it works:
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Starting with Segment AB: You have a segment AB, which is the segment you want to copy.
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Creating Point C: A ray is drawn from point C, which serves as the starting point for the new segment.
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Using a Compass: The distance between points A and B is measured with a compass. This involves placing the compass point on point A and adjusting it so that the other end reaches point B. The compass is then fixed at this width.
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Drawing an Arc: With the compass still set to the length of segment AB, an arc is drawn from point C on the ray. This arc will intersect the ray at point D.
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Locating Point D: The point where the arc intersects the ray from point C is designated as point D.
The construction effectively copies the length of segment AB to create segment CD, since both segments AB and CD are equal to the distance measured by the compass.
This method follows the standard procedure for copying a segment using a compass and straightedge, making it a correct construction technique. The crucial part is that the original length is accurately replicated by the arc drawn with the compass after measuring the original segment. Thus, the answer is yes, the construction demonstrates how to copy a segment correctly by hand.
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