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The tomahawk-shaped instrument shown in the accompanying gure can be used to solve the trisection problem. (PQ = QR = RS, with PTR a semicircle on PR as diameter, UR perpendicular to PS.) If LAOB is the angle to be trisected, place the tomahawk on the angle so that S lies on OA, the line segment UR passes through O, and the semicircle with diameter PR is tangent to OB at T. Prove that the triangles OTQ, ORQ, and ORS are all congruent, whence ZROA is one-third of LAOB. В T R 3 S A

The tomahawk-shaped instrument shown in the accompanying gure can be used to solve the trisection problem. (PQ = QR = RS, with PTR a semicircle on PR as diameter, UR perpendicular to PS.) If LAOB is the angle to be trisected, place the tomahawk on the angle so that S lies on OA, the line segment UR passes through O, and the semicircle with diameter PR is tangent to OB at T. Prove that the triangles OTQ, ORQ, and ORS are all congruent, whence ZROA is one-third of LAOB. В T R 3 S A

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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The tomahawk-shaped instrument shown in the accompanying gure can be used to solve the trisection problem. (PQ = QR = RS, with PTR a semicircle on PR as diameter, UR perpendicular to PS.) If LAOB is the angle to be trisected, place the tomahawk on the angle so that S lies on OA, the line segment UR passes through O, and the semicircle with diameter PR is tangent to OB at T. Prove that the triangles OTQ, ORQ, and ORS are all congruent, whence ZROA is one-third of LAOB. В T R 3 S A
Transcribed Image Text:The tomahawk-shaped instrument shown in the accompanying gure can be used to solve the trisection problem. (PQ = QR = RS, with PTR a semicircle on PR as diameter, UR perpendicular to PS.) If LAOB is the angle to be trisected, place the tomahawk on the angle so that S lies on OA, the line segment UR passes through O, and the semicircle with diameter PR is tangent to OB at T. Prove that the triangles OTQ, ORQ, and ORS are all congruent, whence ZROA is one-third of LAOB. В T R 3 S A
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