compass and straightedge construction of perpendicular
Let be a point and be a line in the Euclidean plane. One can construct a line perpendicular to and passing through . The construction given here yields in any circumstance: Whether or does not matter. On the other hand, the construction looks quite different in these two cases. Thus, the sequence of pictures on the left (in which is in red) is for the case that , and the sequence of pictures on the right (in which is in green) is for the case that .
This construction is justified because and are constructed so that is equidistant from them and thus lies on the perpendicular bisector of .
In the case that , this construction is referred to as dropping the perpendicular from to . In the case that , this construction is referred to as erecting the perpendicular to at .
If you are interested in seeing the rules for compass and straightedge constructions, click on the provided.
|Title||compass and straightedge construction of perpendicular|
|Date of creation||2013-03-22 17:14:01|
|Last modified on||2013-03-22 17:14:01|
|Last modified by||Wkbj79 (1863)|
|Defines||drop the perpendicular|
|Defines||dropping the perpendicular|
|Defines||erect the perpendicular|
|Defines||erecting the perpendicular|