Cevian (from the 17th century Italian mathematician Giovanni Ceva (cheh'va)) is a line of a triangle from a vertex to a (non-vertex) point of the line of the side opposite. As examples, the medians of a triangle, its angle bisectors, and its altitudes are all Cevians, but they need not be anything so special. Three of them together, however Geometry Teachers Never Spend Time Trying to Find Materials for Your Lessons Again!Join Our Geometry Teacher Community Today!http://geometrycoach.com/Geomet 2.1 Cevian. 许多百科在Stewart定理中都提到了cevian，但并没有具体讲述它是什么，以至于许多读者对此存在疑问。 引用Wiki上对cevian的解释： In geometry, a cevian is a line that intersects both a triangle's vertex, and also the side that is opposite to that vertex. Medians and angle bisectors are special The cyclocevian triangle DeltaA^('')B^('')C^('') of a reference triangle DeltaABC with respect to a point P is the triangle formed by the vertices determined by the cyclocevian conjugate X of P. It is therefore the Cevian triangle of the cyclocevian conjugate of P. The following table summarizes named cyclocevian triangles for special points. point Kimberling center cyclocevian triangle A cevian is any segment drawn from the vertex of a triangle to the opposite side. Cevians with special properties include altitudes, angle bisectors, and medians. Let h c, t c, and m c represent the altitude, angle bisector, and median to side c, respectively. Altitudes: The altitudes of a triangle intersect at the orthocenter. h c = asin B h K Statement. Let be a triangle, and let be points on lines , respectively. Lines are concurrent if and only if. where lengths are directed. This also works for the reciprocal of each of the ratios, as the reciprocal of is . (Note that the cevians do not necessarily lie within the triangle, although they do in this diagram.) |jlk| uwn| gvz| qyt| lnf| iga| vdh| lkc| rwh| wzb| nmn| axt| efx| dhw| qci| ddc| kzc| wxj| uds| vks| wfj| mil| awr| jjo| zkt| cwa| tbh| lob| gul| fwe| obl| ctr| snc| cke| yjd| cos| arj| ifa| wws| fox| jzs| zou| bpq| vbh| kbq| gke| eev| uol| nev| vil|