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In Geometry , two Lines are considered perpendicular if one falls on the other in such a way as to create two Equal Angles . The term may be used as a Noun or Adjective . Thus, referring to Figure 1, the line AB is the perpendicular to CD through the point B. If a line is perpendicular to another as in Figure 1, the two angles created are called '' Right Angles '', or ''angles measuring 90°''. The line AB does not have to end at B to be considered perpendicular. Compare to Parallel . NUMERICAL CRITERIA In terms of slopes In a Cartesian Coordinate System , two straight lines and may be described by equations : : as long as neither is Vertical . Then and are the Slopes of the two lines. The lines and are perpendicular if and only if the product of their slopes is -1, or if . CONSTRUCTION OF THE PERPENDICULAR To construct the perpendicular to the line AB through the point P using Compass And Straightedge , proceed as follows (see Figure 2).
To prove that the PQ is perpendicular to AB, use the SSS Congruence Theorem for triangles QPA' and QPB' to conclude that angles OPA' and OPB' are equal. Then use the SAS Congruence Theorem for triangls OPA' and OPB' to conclude that angles POA and POB are equal. SEE ALSO |
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