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说到三角形的边与中线的相互关系,我们就会想到阿波罗尼斯(Apollonius)定理:设AD为△ABC中BC边上的中线,则 2(AB~2+AC~2)=BC~2+4AD~2 阿氏定理虽然揭示了三角形的一条中线与三边间的内在联系,并有很大的实用价值。但遇某些实际问题时仍有一些不便。如已知三条中线求三角形的某边;已知两边上的中线及第三边求其他两边等。在阿氏定理的基础上,我们有三角形的边与中线的几个新关系式。定理已知a、b、c分别为△ABC的∠A、∠B、∠C
When we talk about the relationship between the triangle’s edge and the midline, we think of the Apollonius theorem: Let AD be the midline on the BC side of △ABC, then 2(AB~2+AC~2)=BC~2 The +4AD~2 A’s Theorem reveals the intrinsic link between a triangle’s midline and three sides, and has great practical value. However, there are still some inconveniences in the face of certain practical problems. If you know three sides of the middle line, find the side of the triangle; the middle line on both sides is known and the other side is on the third side. Based on the A’s theorem, we have several new relations between the edges of the triangle and the midline. Theorem knows that a, b, and c are △ABC, ∠A, ∠B, and ∠C, respectively.