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Unformatted text preview: 6-4 PerpendicularsA)Theorem 6-1 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 4-9, 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