近年来,部分地区的中考题中不断出现探索存在型试题,显得新鲜、活泼,它在检测学生的思维、创造,在推进素质教育等方面,确是一类好题型。1 与三角形有关的存在型试题 例1.如图,已知点A在直线l外,点B,C在l上。 (1)若P为△ABC内的任一点,求证:∠P>∠A; (2)试判断在△ABC外,又和点A在直线l的同侧,是否存在一点Q,使∠BQC>∠A,并证明你的结论。 In recent years, the exploration of existing test questions in the examinations in some areas has appeared constantly, appearing fresh and lively. It is indeed a good type of problem in testing student’s thinking and creativity and promoting quality education. 1 Existential test questions related to triangles Example 1. As shown in the figure, it is known that the point A is outside the line l and the point B and C are on the l. (1) If P is any point in △ABC, verify that: ∠P>∠A; (2) Try to determine whether there is a point Q on the same side of line 1 as △ABC and point A, so that ∠BQC >∠A, and prove your conclusion.