Current location - Training Enrollment Network - Mathematics courses - 20 17 Answers to Anhui Mathematics Entrance Examination Paper
20 17 Answers to Anhui Mathematics Entrance Examination Paper
The first answer is definitely wrong, I believe you can see it, because P is an arbitrary point.

The second answer, S2+S4=S 1+S3, is correct. Both of them are equal to half of the whole rectangular area. S2 and S4 have the same base BC, and the sum of the heights of the two triangles is exactly equal to the length AB of the rectangle, S2+S4 =1/2 (AB+BC); S 1 is the same as the base AB of S3, and the sum of the heights of the two triangles is exactly equal to the width BC of the rectangle, and S 1+S3 = 1/2 (AB+BC), so S2+S4=S 1+S3.

The third answer, if S3=2S 1, S4=2S2. When S3=2S 1, it means that the height of triangle PCD is twice that of triangle PAB. At this time, if BC is divided into three parts, the position near B is set to E, and the vertical line of BE intersects with AD at F, then point P can be any point on EF, so there are many situations about the relationship between S4 and S2.

The fourth answer, reduction to absurdity, is that if point P is on the diagonal, then the distance from P to each side is equal, that is to say, the height of triangle S 1 and S2 is equal, and if S 1=S2 and AB=BC, this is impossible.

The correct answer should be: circle 2.