根据附件图片内容，讲解"中心对称等分面积"---能力点 2 中心对称等分面积
**方法总结**
| 条件 | 图示 |
| :----------------------------------------------------------- | :------------------------------------------------------------------- |
| O 为□ABCD 的对称中心,E,F 分别在 AB,CD 上,且 EF 经过对称中心 O | (Diagram of parallelogram ABCD with center O and line EF through O) |
| 结论 | AE=CF, S 四边形AEFD = S 四边形BCFE = 1/2 S □ABCD |
**方法应用**
**例 2** 如图,六边形 ABCDEF 为矩形裁去一块小长方形后的剩余 部分, 请仅用无刻度的直尺画出一条直线 MN, 使得直线 MN 平分六边形 ABCDEF 的面积.
**例 2 题图**
(Diagram of L-shaped hexagon ABCDEF)
**♦ 关键点点拨 ♦**
平分由两个特殊四边形组合而成的图形的面积时,将图形分割为两个特殊四边形, 分别找它们 的对称中心, 作出过它们对称中心的直线即可平分图形的面积.
---
**Diagram Description:**
**Diagram 1 (in Method Summary):**
* Type: Geometric figure (Parallelogram).
* Main Elements:
* Points: Vertices of a parallelogram labeled A, B, C, D in counter-clockwise order. The intersection of diagonals AC and BD is labeled O (center of symmetry). Point E is on side AB, and point F is on side CD.
* Lines: Straight line segments form the sides of parallelogram ABCD. Straight line segments represent the diagonals AC and BD intersecting at O. A straight line segment EF passes through O, connecting side AB to side CD.
* Shapes: Parallelogram ABCD. Triangle AOD, DOC, COB, BOA. Line segment EF. Quadrilateral AEFD and EBCF are formed.
**Diagram 2 (labeled 例 2 题图):**
* Type: Geometric figure (Hexagon / L-shape).
* Main Elements:
* Points: Vertices of a hexagon labeled A, B, C, D, E, F in counter-clockwise order around the boundary. A is at the top-left corner, B is at the bottom-left corner, C is at the bottom-right corner, D is an inner vertex (above C and to the left), E is an inner vertex (above D and to the left), F is an inner vertex (above E and to the left, below A and to the right).
* Lines: Straight line segments form the sides AB, BC, CD, DE, EF, FA. AB appears vertical, BC appears horizontal, CD appears vertical, DE appears horizontal, EF appears vertical, and FA appears horizontal. The corners at B, C, D, E, F, A appear to be right angles.
* Shapes: The shape is an L-shaped hexagon, which is described as the remaining part of a rectangle after cutting off a small rectangle. It can be interpreted as a large rectangle (e.g., formed by vertices A, B, C, and a point above C and to the right of A) from which a smaller rectangle (e.g., with vertices D, E, F, and a point above D and to the right of E) has been removed from a corner. Based on the likely solution method suggested by the hint, this L-shape can be divided into two rectangles by extending one of the interior boundary segments (e.g., extending CD upwards to meet the horizontal line through F and A, or extending DE to the left to meet the vertical line through A and B).