13.3.1.1三角形的内角和-课件-2026-2027学年人教版数学八年级上册

#人教版八年级上册13.3.1.1三角形的内角和专项练习（全文约1500字\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)可直接打印）##知识要点速记1.**三角形内角和定理**：三角形三个内角的和等于$\boldsymbol{180^\circ}$。符号语言：在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleA+\angleB+\angleC=180^\circ$。2.**定理证明思路**：通过作平行线\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)把三个内角转化成一个平角（平行线的性质：内错角相等）。3.**推论1（直角三角形性质）**：直角三角形的两个锐角互余。即在$Rt\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleC=90^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)则$\angleA+\angleB=90^\circ$。4.**推论2**：有两个角互余的三角形是直角三角形。5.**常用解题思想**：-已知两个角\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)直接求第三个角；-角度带比例关系\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)常设未知数$x$列方程求解；-结合高\(\becauseBP、CP\)角平分线\(\becauseBP、CP\)中线综合求角度；-无图题注意分类讨论。⚠️易错提醒：内角和只和三角形形状有关\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)和大小无关。##一\(\becauseBP、CP\)基础过关（判断+填空+选择）###判断题（对√\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)错×）1.一个三角形最多有两个直角。（）2.三角形内角和等于$180^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)与三角形大小无关。（）3.在直角三角形中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)两个锐角之和等于$90^\circ$。（）4.一个三角形最少有两个锐角。（）5.如果三角形两个内角和小于$90^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)那么它是锐角三角形。（）###填空题6.在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleA=50^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleB=60^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)则$\angleC=$______$^\circ$。7.直角三角形一个锐角为$36^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)另一个锐角是______$^\circ$。8.一个三角形三个内角之比为$\(1:2:3\)$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)这个三角形是______三角形。9.在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleA:\angleB:\angleC=2:3:4$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)则$\angleA=$______$^\circ$。10.在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleA=45^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleB=\angleC$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)则$\angleB=$______$^\circ$。###选择题11.在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleA=70^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleB=50^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)则$\angleC$等于（）A.$40^\circ$B.$50^\circ$C.$60^\circ$D.$70^\circ$12.下列角度\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)不可能是同一个三角形三个内角的是（）A.$50^\circ,60^\circ,70^\circ$B.$90^\circ,35^\circ,55^\circ$C.$100^\circ,40^\circ,40^\circ$D.$80^\circ,80^\circ,30^\circ$13.一个三角形\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)两个内角之和等于第三个内角\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)这个三角形是（）A.锐角三角形B.直角三角形C.钝角三角形D.等腰三角形14.在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleA=2\angleB$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleC=60^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)则$\angleA$的度数为（）A.$60^\circ$B.$80^\circ$C.$100^\circ$D.$120^\circ$##二\(\becauseBP、CP\)中档解答题15.在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)已知$\angleA=48^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleB=72^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)求$\angleC$的度数。16.一个三角形三个内角的度数比是$\(2:3:5\)$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)求三个内角分别是多少度\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)并判断三角形的类型。17.在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$AD$是$BC$边上的高\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleB=50^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleBAD=40^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleC=60^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)求$\angleDAC$的度数。18.在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$AE$平分$\angleBAC$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleB=45^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleC=55^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)求$\angleBAE$的度数。##三\(\becauseBP、CP\)拓展提升题19.在$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleA-\angleB=20^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleC=60^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)求$\angleA$\(\becauseBP、CP\)$\angleB$的度数。20.已知$\triangleABC$中\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleABC$与$\angleACB$的角平分线交于点$P$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\angleA=60^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)求$\angleBPC$的度数。##参考答案1.×（两个直角相加已经是$180^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)不能构成三角形）2.√3.√4.√5.×（两个内角和小于$90^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)第三个角大于$90^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)是钝角三角形）6.$70$7.$54$8.直角9.$40$10.$\(67.5\)$11.A12.D（$80+80+30=190^\circ\neq180^\circ$）13.B14.B15.解：$\because\angleA+\angleB+\angleC=180^\circ$$\therefore\angleC=180^\circ-48^\circ-72^\circ=60^\circ$答：$\angleC=60^\circ$。16.解：设三个内角为$\(2x,3x,5x\)$$2x+3x+5x=180^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$10x=180^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$x=18^\circ$$2x=36^\circ\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)3x=54^\circ\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)5x=90^\circ$有一个角是$90^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)是直角三角形。答：三个内角为$36^\circ\(\becauseBP、CP\)54^\circ\(\becauseBP、CP\)90^\circ$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)直角三角形。17.解：$\becauseAD$是高\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)$\therefore\angleADC=90^\circ$$\angleDAC=90^\circ-\angleC=90^\circ-60^\circ=30^\circ$答：$\angleDAC=30^\circ$。18.解：$\angleBAC=180^\circ-\angleB-\angleC=180^\circ-45^\circ-55^\circ=80^\circ$$\becauseAE$平分$\angleBAC$$\therefore\angleBAE=\dfrac12\angleBAC=40^\circ$答：$\angleBAE=40^\circ$。19.解：$\begin{cases}\angleA-\angleB=20^\circ\\\angleA+\angleB=180^\circ-60^\circ=120^\circ\end{cases}$两式相加：$2\angleA=140^\circ\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)\angleA=70^\circ$$\angleB=120^\circ-70^\circ=50^\circ$答：$\angleA=70^\circ\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)\angleB=50^\circ$。20.解：$\because\angleA=60^\circ$$\therefore\angleABC+\angleACB=180^\circ-60^\circ=120^\circ$$\becauseBP\(\becauseBP、CP\)CP$是角平分线$\therefore\anglePBC=\dfrac12\angleABC\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)\anglePCB=\dfrac12\angleACB$$\anglePBC+\anglePCB=\dfrac12(\angleABC+\angleACB)=60^\circ$$\angleBPC=180^\circ-60^\circ=120^\circ$答：$\angleBPC=120^\circ$。##解题小结1.核心公式：$\angleA+\angleB+\angleC=180^\circ$；直角三角形两锐角互余；2.比例题型：设未知数$x$\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)列方程是最稳妥方法；3.综合题经常搭配**角平分线\(\becauseBP、CP\)高**一起考\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)先找直角\(\becauseBP、CP\)等角；4.模型：三角形两个内角平分线夹角$\angleBPC=90^\circ+\dfrac12\angleA$（可以直接记住\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)选择填空提速）。下一节是**三角形的外角**\(2\angleA=140^\circ\(\angleA=70^\circ\(\therefore\anglePBC=\dfrac12\angleABC，\anglePCB=\dfrac12\angleACB\)\angleB=50^\circ\)\angleA=70^\circ\)要不要直接给你13.3.1.2的专项练习？人教版数学（新教材）八年级上册13.3.1.1三角形的内角和授课教师：.

班

级：

8年级（

）班.

时

间：.

2026/11/1

第十三章三角形

我命由我不由天，是魔是仙，我自己说了算。少年不必畏惧难题与非议，沉下心勤学笃行，不认命、不服输，用汗水改写前路，活出属于自己的光彩。1.探索并证明三角形的内角和定理.(重、难点)2.三角形内角和定理及其运用.(重点)3.学会解决与求角度有关的实际问题.4.体会转化的数学思想.请你帮忙评判一下这些关于三角形内角和的观点！我是钝角三角形，我有一个钝角，我的内角和最大！我是直角三角形，我的形状最大，我的内角和肯定最大！我是锐角三角形，我的形状最小，我的内角和也最小！问题1

在小学我们已经知道任意一个三角形的三个内角的和等于180°，你还记得是怎么发现这个结论的吗？请大家借助手中的三角形纸片，回忆小学时的学习经历.1.用度量的方法得出结论.与边一样，三角形的角也是构成三角形的元素。本节我们学习三角形的三个内角之间的关系。在小学，通过度量或剪拼，我们已经知道三角形的内角和等于180°，这样的方法获得的结论可靠吗？由于测量常常有误差，这样验证三角形的内角和等于180°，不能完全令人信服；又由于形状不同的三角形有无数个，我们不可能用上述方法一一验证所有三角形的内角和等于180°.因此，需要通过推理的方法去证明：任意一个三角形的内角和等于180°.探究：你还记得在小学是如何通过剪拼的方法得出三角形的内角和吗？下图给出了两种剪拼的方法。从这个操作过程中，你能发现证明的思路吗？在图(1)中，将△ABC的∠B和∠C剪下，分别拼在∠A的左右，三个角合起来形成一个平角，出现一条过点的直线，移动后的∠B和∠C各有一条边在直线l上。想一想，直线l与△ABC的边BC有什么关系？你能由这个图想出证明“三角形的内角和等于180”的方法吗？由上述拼合过程得到启发，过△ABC的顶点A作直线l平行于△ABC的边BC.由平行线的性质与平角的定义就能证明“三角形的内角和等于180°”这个结论。ABC24153

l证明：如图所示，过点A作直线l，使l//BC．∵l//BC，∴∠2=∠4,（两直线平行，内错角相等）同理，∠3=∠5.

∵∠1，∠4，∠5组成平角∴∠1+∠4+∠5=180°,（平角定义）∴∠A+∠B+∠C=180°.（等量代换）∴任意一个三角形的内角和都等于180°已知：△ABC（如图所示）．求证：∠A+∠B+∠C=180°．以上我们就证明了任意一个三角形的内角和都等于180°，得到如下定理：三角形内角和定理：

三角形的三个内角和等于180°即：∠A+∠B+∠C=180°知识点1

三角形内角和定理

C（第1题）

返回（第2题）

A

C

返回

返回试一试：由图（2），你能给出这个定理的其他证法吗？证明：如图，延长BC，过点C作直线l，使l//AB．∵l∥AB，∴∠1＝∠4（两直线平行，内错角相等），∠2＝∠5（两直线平行，同位角相等）．∵∠3，∠4，∠5组成平角，∴∠3＋∠4＋∠5＝180°（平角定义）．∴∠1＋∠2＋∠3＝180°（等量代换）．ABC123l54试一试：由图（2），你能给出这个定理的其他证法吗？例1：如图，在△ABC中，∠BAC=40°,∠B=75°，AD是△ABC的角平分线．求∠ADB的度数．CBDA

例2：如图，是A、B、C三岛的平面图.C岛在A岛的北偏东50°方向，B岛在A岛的北偏东80°方向，C岛在B岛的北偏西40°向．从B岛看A，C两岛的视角∠ABC是多少度？从C岛看A，B两岛的视角∠ACB呢？北北CABDE分析