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平行四边形的判定可从边入手,如一组对边平行且相等、两组对边平行或相等:也可从角入手,如两组对角相等、两组邻角互补等.学生自然会考虑能否从角、边同时给出条件来判定平行四边形,于是就有了如下的问题.问题:一组对边和一组对角分别相等的四边形是不是平行四边形?答案是不一定.肯定的实例中最简单的是正方形.两个相对的角是直角,两条相对的边相等.至于否定的实例,人们也很早就给出了:(1)作△ABC,使AB=AC,(2)在BC上取一点E,使EB>EC,(3)以点A为圆心,EC为半径作弧,
The determination of a parallelogram can start from the side, such as a parallel and equal pairs of sides, parallel or equal to the two sides of the pair: you can also start from the angle, such as the two groups of equal angles, two adjacent groups complement each other, etc. Students will naturally consider Whether the parallelogram is given at the same time from the angle and the edge gives rise to the following problems: Question: Is a set of parallelograms with a pair of diagonals equal to each other not parallel? The answer is not certain. The simplest of these is a square. The two opposite corners are right angles, and the two opposite sides are equal. As for the negative example, one has also given very early: (1) ABC, making AB = AC, (2 ) Take a point E on BC to make EB> EC, (3) Take the point A as the center and EC as the arc for the radius,