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2014年的北京中考24题,是一道基于正确作图的几何综合题,如果同学们对轴对称的概念掌握不好,那么本题的求解将受阻.下面,我们先一起阅读原题:24.在正方形ABCD外侧作直线AP,点B关于直线AP的对称点为E,连接BE,DE,其中DE交直线AP于点F.(1)依题意补全图1;(2)若∠PAB=20°,求∠ADF的度数;(3)如图2,若45°<∠PAB<90°,用等式表示线段AB,FE,FD之间的数量关系,并证明.
24 questions in the Beijing exam 24 in 2014, is a geometric synthesis based on the correct mapping, if students do not grasp the concept of axisymmetric, then the problem solving will be blocked. Now, we first read the original title: 24. The outer side of the square ABCD for a straight line AP, point B on the straight line AP symmetry point E, connect BE, DE, where DE intersects the line AP at point F. (1) Complementing Figure 1 according to the intended meaning; (2) If ∠ PAB = 20 °, find the degree of ADF; (3) As shown in Figure 2, if 45 ° <∠ PAB <90 °, use the equation to express the relationship between the number of segments AB, FE, FD and prove.