P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.

Explanation

To show that line segment PQ is bisected at point O, we will use the properties of triangles and congruence.

### Step-by-Step Solution:

1. **Draw the Parallelogram and Points**:
- Start by drawing parallelogram ABCD. Label the points A, B, C, and D in a clockwise manner.
- Mark points P and Q on sides AD and BC respectively, such that line segment PQ passes through point O, the intersection of diagonals AC and BD.

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