AMSCO'S Geometry. New York - Rye High School

Basic Constructions 201Construction 6Construct a Line Perpendicular to a GivenLine Through a Point Not on the Given Line.Given Point P not on .ConstructPE g ' AB g AB g CPPPACDBACDEBACFDEB1. With P as center and anyconvenient radius, draw anarc that intersects AB gintwo points, C and D.2. Open the compass to aradius greater than onehalfof CD. With C and Das centers, draw intersectingarcs. Label the point ofintersection E.3. Draw PE gintersecting AB gat F.PAFDBConclusionPE g ' AB gEProof Statements Reasons1. CP > PD, CE > DE1. Radii of congruent circles arecongruent.2. CP PD, CE DE 2. Segments that are congruent havethe same measure.3. PE g ' CD3. If two points are each equidistantfrom the endpoints of a line segment,then the points determine the perpendicularbisector of the line segment.(Theorem 5.2)4. PE g ' AB g4. CD is a subset of line AB g.