1引言已知“一组对角相等、一组对边相等的四边形是平行四边形”是假命题,在教学时我们都强调过不能以此作为平行四边形的判定依据,但有不少同学会感到困惑,更有甚者在解决问题时甚至以此作为判定依据加以运用,此时简单、有效地举出反例,成为破解困惑、防止犯错的关键.本文从等腰梯形展开论述,进而给出了从三角形入手,利用尺规作图法构造“一组对角相等、一组对边相等的四边形是平行四边形”反例的简单、有效方法.通过反例的构造,我们从另一个层 1 Introduction It is known that “a set of diagonals are equal and a set of parallelograms whose sides are equal are parallelograms.” It is a fake proposition that we all stressed during teaching that we can not judge this as a parallelogram. However, many students Will be confused, and some even in the solution to the problem or even to use as a basis for judgment, then simply and effectively cited counter-example, become the key to crack the puzzle and prevent mistakes.This paper starts from the isosceles trapezoid discussion, and then to Starting from the triangle, using rulers to construct a simple and efficient method of constructing a set of diagonals equal to one pair of quadrilateral equal sides is a parallelogram, we construct a counterexample from the other layer