The image contains mathematical problems related to geometry, specifically concerning trapezoids and their properties. Here’s a summary of the questions presented in the problems:

1. **Trapezoid Properties**: Prove a certain relation about the heights and sides of trapezoid ABCD where AB is parallel to CD and AB is shorter than CD.

2. **Angle Calculations and Relations**:
- Prove that angles and segments intersect and maintain certain equalities.
- Calculate specific angles based on given conditions.

3. **Orthogonal Lines**: Determine properties of right angles within the context of the trapezoid.

4. **Area Calculations**: Calculate the area of trapezoid ABCD given specific dimensions and angle conditions.

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