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2. Every angle can be trisected using a compass and marked straightedge. The following construction is due to Archimedes. Assume the compass has two marks on it, a distance r apart. Let ZBAC be an angle. Draw a circle y of radius r and center A. The circle will intersect both sides of the angle; in order to simplify the notation let us assume that B and C lie on the circle. Place the straightedge so that it passes through C and so that one mark is at a point D on y and the other is at a point E on `AB. (See Figure 9.17.) Use the Isosceles Triangle Theorem and the Euclidean Angle Sum Theorem to prove that u(2CEB) = (1/3)µ(LCAB). FIGURE 9.17: Archimedes' trisection using a marked straightedge

2. Every angle can be trisected using a compass and marked straightedge. The following construction is due to Archimedes. Assume the compass has two marks on it, a distance r apart. Let ZBAC be an angle. Draw a circle y of radius r and center A. The circle will intersect both sides of the angle; in order to simplify the notation let us assume that B and C lie on the circle. Place the straightedge so that it passes through C and so that one mark is at a point D on y and the other is at a point E on `AB. (See Figure 9.17.) Use the Isosceles Triangle Theorem and the Euclidean Angle Sum Theorem to prove that u(2CEB) = (1/3)µ(LCAB). FIGURE 9.17: Archimedes' trisection using a marked straightedge

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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2. Every angle can be trisected using a compass and marked straightedge. The following construction is due to Archimedes. Assume the compass has two marks on it, a distance r apart. Let ZBAC be an angle. Draw a circle y of radius r and center A. The circle will intersect both sides of the angle; in order to simplify the notation let us assume that B and C lie on the circle. Place the straightedge so that it passes through C and so that one mark is at a point D on y and the other is at a point E on `AB. (See Figure 9.17.) Use the Isosceles Triangle Theorem and the Euclidean Angle Sum Theorem to prove that u(2CEB) = (1/3)µ(LCAB). FIGURE 9.17: Archimedes' trisection using a marked straightedge
Transcribed Image Text:2. Every angle can be trisected using a compass and marked straightedge. The following construction is due to Archimedes. Assume the compass has two marks on it, a distance r apart. Let ZBAC be an angle. Draw a circle y of radius r and center A. The circle will intersect both sides of the angle; in order to simplify the notation let us assume that B and C lie on the circle. Place the straightedge so that it passes through C and so that one mark is at a point D on y and the other is at a point E on `AB. (See Figure 9.17.) Use the Isosceles Triangle Theorem and the Euclidean Angle Sum Theorem to prove that u(2CEB) = (1/3)µ(LCAB). FIGURE 9.17: Archimedes' trisection using a marked straightedge
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