id: 06560939
dt: j
an: 2016c.00754
au: Contreras, José N.
ti: Discovering, applying, and extending Ceva’s theorem.
so: Math. Teach. (Reston) 108, No. 8, 632-637 (2015).
py: 2015
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: G45 G75 U75
ut: geometry; Ceva’s theorem; triangles; cevians; division points; ratios;
concurrence; proofs; similarity; centroid; medians; orthocenter;
altitudes; incenter; angle bisectors; circumcenter; perpendicular
bisectors; interior angle bisector theorem; medial triangle; points of
concurrency; Gergonne point; Nagel point; Lemoine point; Fermat point;
generalization; polygons with an odd number of sides
ci:
li: http://www.nctm.org/Publications/mathematics-teacher/2015/Vol108/Issue8/Discovering,-Applying,-and-Extending-Ceva_s-Theorem/
ab: From the text: Among the most commonly known points of concurrency are the
four points of intersection classically associated with a triangle: the
centroid, the orthocenter, the incenter, and the circumcenter. Armed
with two extremely powerful theorems from elementary geometry ‒
Ceva’s theorem and its converse, here referred to simply as Ceva’s
theorem ‒ I take my college geometry class on a journey to simplify
and unify the proofs of classical concurrency theorems.
rv: