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如图1所示的图形ABPC,其形状类似于圆规,故称之为“规形图”.规形图有下列一个极为重要的结论:∠BPC=∠A+∠B+∠C.下面,我们先来验证这一重要结论.思路1:利用三角形的内角和等于180°.如图2,连接BC.在△ABC中,因为∠A+∠4BC+∠A CB=180°,∠A+∠ABP+∠ACP+∠PBC+∠PCB=180°.所以∠PBC+∠PCB=180°-∠A-∠ABP-∠ACP=180°-∠A-∠B-∠C.在△PBC中,因为∠BPC+∠PBC+∠PCB=180°,所以∠BPC+180°-∠A-∠B-∠C=180°,∠BPC=∠A+∠B+∠C.
The graph ABPC, shown in Figure 1, has a shape similar to that of a compass, so it is called a “graph.” The graph has the following important conclusion: ∠BPC = ∠A + ∠B + ∠C. Let’s first verify this important conclusion: Idea 1: Use the interior angle of the triangle and equal to 180 °. Connect BC in Figure 2. In △ ABC, because ∠A + ∠4BC + ∠A CB = 180 °, ∠A + ∠ABP + ∠ ACP + ∠PBC + ∠PCB = 180 ° Therefore, ∠PBC + ∠PCB = 180 ° -∠A-∠ABP-∠ACP = 180 ° -∠A-∠B-∠C. In ΔPBC, since ∠BPC + ∠PBC + ∠ PCB = 180 °, so ∠BPC + 180 ° -∠A-∠B-∠C = 180 °, ∠BPC = ∠A + ∠B + ∠C.