When Mac was asked to duplicate Angle TAR, he used his protractor to measure angle TAR and then to make Angle MAC. Is his construction correct? Explain.
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Final answer:
Mac was somewhat correct in utilizing a protractor to duplicate angle TAR. However, in geometric construction, angles are usually duplicated using a compass and straight edge.
Explanation:
In terms of duplicating angle TAR to create angle MAC, Mac was somewhat correct in his use of a protractor to measure and recreate the angle. However, the exact correctness of his construction could be contingent upon additional elements. In simple terms, yes, you can duplicate an angle by using a protractor. You would simply need to measure the degree of the original angle and then replicate this on a separate point using the same degree measurement. Nonetheless, in proper geometric construction, an angle is duplicated using a compass and a straight edge rather than a protractor.
For instance, if Angle TAR measures 30 degrees, Mac will set his protractor at an intersect point M to measure and create angle MAC, that also measures 30 degrees. It's essential to note that while the measure of the angles are identical, the lengths of the sides of the angles will not necessarily be identical unless defined to be so.
Yet, using a protractor is not necessarily the exact method of angle duplication as described in classic geometric construction. There, one uses a compass and straightedge to duplicate an angle. This process generally involves drawing an initial line, creating an arc crossing the angle's sides with a compass, and then duplicating this arc on the other line to assure both angles are comparable.
Learn more about Angle Duplication here:
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A.
xyz(y2z + y + 1)
*
B.
xy2z(yz + 1 + 1)
*
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*
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