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已知:如图1,在凹四边形ABCD中,求证;∠BDC=∠A+∠B+∠C. 分析;利用三角形外角性质和平行线的性质可探索出多种添辅助线的方法: 方法1:连接AD并延长(如图2)由外角性质易证方法2:连接BC(如图3)由三角形内角和的定理易证
Known: As shown in Figure 1, in the concave quadrangle ABCD, verify; ∠BDC = ∠A + ∠B + ∠C. Analysis; use the nature of the triangular triangle and the properties of the parallel lines to explore a variety of ways to add an auxiliary line: Method 1: Connected to AD and extended (Figure 2) by the nature of the outer corners easily proven method 2: connecting BC (Figure 3) by the triangle inside the angle of the theorem