An auxiliary line (or helping line) is an extra
line needed to complete a
proof in
plane geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms ...
. Other common auxiliary constructs in elementary plane synthetic geometry are the helping circles.
As an example, a proof of the theorem on the
sum of angles of a triangle can be done by adding a straight line parallel to one of the triangle sides (passing through the opposite vertex).
Although the adding of auxiliary constructs can often make a problem obvious, it's not at all obvious to discover the helpful construct among all the possibilities, and for this reason many prefer to use more systematic methods for the solution of geometric problems (such as the coordinate method, which requires much less ingenuity).
References
External links
*http://www.cut-the-knot.org/Generalization/MenelausByEinstein.shtml On Einstein's opinion regarding proofs that use the introduction of additional constructs
Geometry
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