某地九年级竞赛试卷中有如下一则关于梯形的赛题:已知:如图1,梯形ABCD中,AD∥BC,梯形四内角的角平分线AE、BG、CG、DE相交构成四边形HEFG,HF⊥GE,垂足为N.求证:梯形ABCD是等腰梯形.分析证明一个梯形是等腰梯形的常见方法是证明这个梯形两腰相等或者同一底边上的两底角相等或者对角线相等.梯形常见的辅助线添法有作高线、平移一腰、平移对角线、 It is known that in the ninth grade contest paper of a certain place, a trapezoidal question is as follows: It is known that as shown in FIG. 1, trapezoid ABCD, the angle bisector AE, BG, CG, DE of AD∥BC and trapezoidal inner corners intersect each other to form a quadrilateral HEFG , HF⊥GE, foot drop is N. Proof: trapezoidal ABCD isosceles trapezoid.An analysis of a trapezoidal isosceles trapezoid is a common method to prove that this trapezoid equal or two bottom corners of the same bottom of the same or diagonal The same line trapezoidal common auxiliary line Tim method for high line, translation of one waist, translation diagonal,