To determine whether the quadrilaterals with the side lengths of 3, 6, 7, and 8 inches are identical or not, we need to examine the sets of side lengths provided.
Let's note the side lengths for each quadrilateral listed:
- Quadrilateral 1: 4, 6, 8, 7 (sides: 4, 6, 7, 8 inches)
- Quadrilateral 2: 7, 8, 3, 6 (sides: 3, 6, 7, 8 inches)
- Quadrilateral 3: 7, 3, 8, 6 (sides: 3, 6, 7, 8 inches)
- Quadrilateral 4: 3, 6, 8, 7 (sides: 3, 6, 7, 8 inches)
Now, let's identify the quadrilaterals that have the side lengths of 3, 6, 7, and 8 inches:
- Quadrilateral 2: 3, 6, 7, 8
- Quadrilateral 3: 3, 6, 7, 8
- Quadrilateral 4: 3, 6, 7, 8
So, the quadrilaterals with side lengths of 3, 6, 7, and 8 inches are Quadrilaterals 2, 3, and 4.
Quadrilateral 1 does not have the correct side lengths, as it includes a side of 4 inches, which does not match the other three mentioned.
Lastly, regarding whether they are identical or not:
Since the side lengths of Quadrilaterals 2, 3, and 4 are the same (3, 6, 7, 8) and can be rearranged to form the same quadrilateral, they are identical in terms of side lengths. However, their actual shapes could differ, depending on angles, so that aspect can't be definitively confirmed without additional information.
To summarize, the quadrilaterals that have the same side lengths of 3, 6, 7, and 8 inches are: Quadrilaterals 2, 3, and 4.