In this problem, we have a rectangular piece of fabric with dimensions $44$ inches by $16$ inches. The question is about the possible congruent shapes that can be created by making a single straight cut.

Analysis of Options:

1. 2 Rectangles:

   • A single straight cut along the middle of either dimension (either cutting the 44-inch side into two 22-inch parts or the 16-inch side into two 8-inch parts) will produce two congruent rectangles.
   • This option is correct.

2. 3 Rectangles:

   • A single straight cut cannot produce three rectangles from a single rectangle.
   • This option is incorrect.

3. 2 Right Triangles:

   • A diagonal cut from one corner of the rectangle to the opposite corner will split the fabric into two right triangles of equal size.
   • This option is correct.

4. 3 Right Triangles:

   • A single cut cannot produce three triangles from a single rectangle.
   • This option is incorrect.

5. 2 Right Trapezoids:

   • It is not possible to create two congruent trapezoids from a single rectangle with a single straight cut.
   • This option is incorrect.

6. 3 Right Trapezoids:

   • Similarly, a single cut cannot produce three trapezoids.
   • This option is incorrect.

Final Answer:

The correct choices are:

• a. 2 rectangles
• c. 2 right triangles

Would you like more details on this solution or have any questions?

Here are 5 additional related questions you may find useful:

1. What other shapes can be formed if more cuts are allowed?
2. How can we calculate the area of each resulting shape?
3. What would happen if we cut diagonally but not from corner to corner?
4. How does the orientation of the cut affect the congruency of the shapes?
5. Can we form non-right triangles from a single cut?

Tip: For rectangle division, remember that cuts along the width or length always yield rectangles, and diagonal cuts can yield triangles!