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The problem asks to identify which quadrilateral could be proved to be a parallelogram by Theorem 6.2D, which states that a quadrilateral is a parallelogram if both pairs of consecutive angles are supplementary (i.e., their sum is \(180^\circ\)).

### Analysis of Quadrilaterals:
1. **ABCD**: This quadrilateral shows equal opposite sides (parallelogram property), but there's no clear indication of supplementary angles.
   
2. **EFGH**: The angles labeled as \(180^\circ - x\) and \(x\) indicate consecutive angles that sum to \(180^\circ\). This satisfies the condition of Theorem 6.2D that consecutive angles must be supplementary.

3. **IJKL**: It appears to be a rhombus-like shape, but there is no explicit information about consecutive angles being supplementary.

4. **MNOP**: Diagonals intersect, but there’s no information about angles.

5. **QRST**: It has some angle measures, but none show consecutive angles summing to \(180^\circ\).

### Conclusion:
The quadrilateral **EFGH** is the one that satisfies the conditions of Theorem 6.2D since it shows consecutive angles that are supplementary.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. What are the properties of a parallelogram?
2. How do you prove a quadrilateral is a parallelogram?
3. What other theorems can be used to prove a quadrilateral is a parallelogram?
4. How does the property of supplementary angles apply to trapezoids?
5. What are the differences between a rhombus and a parallelogram?

**Tip**: Always check if both pairs of opposite sides and angles meet the parallelogram properties when solving quadrilateral proofs.

Which quadrilateral shown could be proved to be a parallelogram by Theorem 6.2D (Quad with consecutive angles supplementary to both consecutive angles)?

Identify which quadrilateral can be proved as a parallelogram using Theorem 6.2D, which states that a quadrilateral is a parallelogram if both pairs of consecutive angles are supplementary. Suitable for students in Grades 9-10.

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