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Unformatted text preview: 64 PerpendicularsA)Theorem 61 a.In a given plane, through a given point of a given line, there is one and only one line perpendicular to the given lineb.Proof:i.Restatement: Let E be a plane, let L be a line in E, and let P be a point of L.1.Existence) there is a line M in E such that M contains P and M is perpendicular to L 2.Uniqueness) there in only one such line M3.Proof of (1) a.Let H be one of the two half planes in E, determined by L, and let X be any point of L, other than P. The Angle Construction Postulate asserts that there exists a ray , with Y in H, such that . Let M = . Then at P.4.Proof of (2) a.Suppose that both M and R are perpendicular to L at P. We will try to prove that M = Ri.M and R contain rays and with and ii.By the definition of perpendicular and Theorem 49, both of the angles and are right anglesiii.The Angle Construction Postulate asserts that there is only one ray , with Y in H, such that iv.and are the same rayv.Since M and R have more that one point in...
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This note was uploaded on 05/16/2011 for the course ALGEBRA 098 taught by Professor Johnson during the Spring '09 term at Grand Valley State.
 Spring '09
 Johnson
 Algebra

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