To determine if quadrilateral WXYZ can be a parallelogram, we need to ensure that both pairs of opposite sides are congruent, which means they should be equal in length.
1. Option 1: One pair of sides measuring 15 mm and the other pair measuring 9 mm.
- For a figure to be a parallelogram, opposite sides must be equal.
- If one pair of sides is 15 mm and the other pair is 9 mm, this scenario meets the criteria for a parallelogram since both pairs of opposite sides can be congruent (one pair is 15 mm and another pair is 9 mm).
- Therefore, WXYZ can indeed be a parallelogram in this case.
2. Option 2: One pair of sides measuring 15 mm and the other pair measuring 7 mm.
- Again, for a figure to be a parallelogram, the opposite sides must be equal.
- If one pair of sides is 15 mm and the other pair is 7 mm, this does not satisfy the parallelogram property because the pairs of opposite sides are not congruent.
- Thus, WXYZ cannot be a parallelogram in this scenario.
3. Option 3: WXYZ cannot be a parallelogram because there are three different values for [tex]\( x \)[/tex] when each expression is set equal to 15.
- If setting up equations to determine the side lengths leads to different values for [tex]\( x \)[/tex], it indicates inconsistency in the side measurements.
- This inconsistency means that the opposite sides cannot be congruent, therefore disqualifying WXYZ as a parallelogram.
4. Option 4: WXYZ cannot be a parallelogram because the value of [tex]\( x \)[/tex] that makes one pair of sides congruent does not make the other pair of sides congruent.
- If the value of [tex]\( x \)[/tex] that ensures one pair of sides is equal doesn't coincide with the value of [tex]\( x \)[/tex] for the other pair, there would be a mismatch in the opposite sides.
- Therefore, WXYZ cannot be a parallelogram in this scenario, as it fails the property of having both pairs of opposite sides being equal.
From the detailed checking, it is clear that Option 1 best explains if quadrilateral WXYZ can be a parallelogram. Thus, WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.
