Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.

Explanation

To prove that the areas of two parallelograms on the same base and between the same parallels are equal using vectors, we can follow these steps:

### Step 1: Define the Parallelograms
Let’s consider two parallelograms, ABCD and DECF, where:
- AB is the base of both parallelograms.
- The lines AD and BC are parallel to each other, and DE is parallel to AB.

### Step 2: Assign Vectors
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