三角形外角定理公式-三角形外角定理公式

maths 啊，咱不讲那些教科书里像念经一样死的定义。三角形外角定理，说白了就是啥叫“外角等于不相邻两个内角之和”。
这公式看着顺眼，实际用起来可跟背课文不忒一样，你得把脑袋凑到概念边上，看着图找魂。 先看图，画个三角形 ABC，随意挑个点 D 在边 AC 的延长线上，连起来 BD。
这时候外角就是那个 ∠BDC。它等于哪两个角加起来呢？就是 ∠A 和 ∠B。
这俩角，一个在内部，一个在外部，就像天平两边对拉，把其中一半翻出来，正好拼成那个外角。 为啥要强调“不相邻”？这词儿别看干瘪，但透着意思。
要是涉及到共顶点的那个内角，那可不中了，那是内角和外角自己打架，没法算。得找那两个真正的路人甲、路人乙，就是跟这条边没直接相连的两个角。 这就好比你在马路中间开车，外面有个路口，新开了个车道，通往你后方的路口，你走进去，回头看看，你后方的路口角度，正好等于你左边和右边两条路交汇的角之和。自然，这话忒抽象了，咱得给点数据看看脑子转得快不快。 假设你拿个尺子量个直角三角形，一条直角边是 3 厘米，另一条直角边是 4 厘米，斜边就是 5 厘米。在直角顶点处画外角。
那斜边上的内角是 90 度减去一个角，另一条直角边上的内角是 90 度另一个角。
这两个加起来，不就是 180 度减去 90 度吗，等于 90 度。外角嘛，就是一个锐角三角形的外角，肯定比直角小。 我再举个数，这更直观。画个直角梯形，上底 4，下底 6，高 3。分割一下，变成个直角三角形、个等腰梯形、个长方形。
看中间那个小直角三角形，底边是 1，高是 3，斜边就是 $sqrt{1^2 + 3^2} = sqrt{10}$，约等于 3.16。
那它的底角是多少度？反正反正反正，反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反正反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