如图所示，ABCD 是一个由四个三角形组成的长方形。
三角形 ABF 的面积与长方形的面积之比为 1 : 9。
三角形 AFE 的面积与长方形的面积之比为 1 : 6。 下列哪些陈述是正确的？ 陈述 A：三角形 ABF 的面积与三角形 AFE 的面积之比为 2 : 3。
陈述 B：ED 是三角形 EFD 的底，其对应的高是 EF。
陈述 C：三角形 ABF 和 DFC 的面积之和等于三角形 AFE 和 EFD 的面积之和。

1. Evaluate Statement A by comparing the given area ratios.

The ratio of the area of triangle ABF to the rectangle is $1 : 9$, and the ratio of the area of triangle AFE to the rectangle is $1 : 6$.
Ratio of Area(ABF) to Area(AFE) = $\frac{1}{9} : \frac{1}{6} = \frac{2}{18} : \frac{3}{18} = 2 : 3$.
Statement A is true.

2. Evaluate Statement B by identifying the correct height for base ED in triangle EFD.

For triangle EFD, if ED is taken as the base, the corresponding height is the perpendicular distance from the opposite vertex F to the line containing ED (which is AD). This perpendicular distance is the length of the rectangle (AB or DC), not the length of the segment EF.
Statement B is false.

3. Evaluate Statement C by calculating the sum of the areas of the respective triangles.

Let the length of the rectangle be $L$ (AB = DC) and the width be $W$ (AD = BC).
Area of $\triangle ABF$ + Area of $\triangle DFC$ = $\frac{1}{2} \times L \times BF + \frac{1}{2} \times L \times FC = \frac{1}{2} \times L \times (BF + FC) = \frac{1}{2} \times L \times W = \frac{1}{2}$ Area of rectangle.
Area of $\triangle AFE$ + Area of $\triangle EFD$ = $\frac{1}{2} \times L \times AE + \frac{1}{2} \times L \times ED = \frac{1}{2} \times L \times (AE + ED) = \frac{1}{2} \times L \times W = \frac{1}{2}$ Area of rectangle.
Since both sums equal half the area of the rectangle, they are equal.
Statement C is true.

4. Conclude which option is correct.

Since Statements A and C are true, the correct option is (3).