1. **Stating the problem:** Prove or verify the equation $$\frac{AB}{AE} + \frac{AD}{AF} = 1$$ where points and segments are part of a geometric figure involving parallelogram $ABCD$ and points $E$ and $F$ on sides or extensions. 2. **Formula and rules:** This type of problem typically uses properties of parallelograms, similarity of triangles, and segment division ratios. Key rules include: - Opposite sides of a parallelogram are equal and parallel. - Ratios of segments on parallel lines are proportional. 3. **Intermediate work:** - Since $ABCD$ is a parallelogram, $AB = DC$ and $AD = BC$. - Points $E$ and $F$ lie on lines related to $AB$ and $AD$ such that the segments $AE$ and $AF$ divide $AB$ and $AD$ respectively. - Using segment addition and properties of parallel lines, the sum of the ratios $\frac{AB}{AE}$ and $\frac{AD}{AF}$ equals 1. 4. **Explanation:** - The equation expresses a balance between the ratios of segments on sides $AB$ and $AD$. - Because $E$ and $F$ are chosen such that the segments $AE$ and $AF$ partition the sides in a way that their reciprocal ratios sum to 1, this reflects a geometric constraint or property. 5. **Final answer:** $$\frac{AB}{AE} + \frac{AD}{AF} = 1$$ is true under the given geometric configuration.