To determine if quadrilateral WXYZ can be a parallelogram, we need to analyze the given side measurements and understand the conditions required for a quadrilateral to be a parallelogram.
A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent. Let's evaluate each option to determine if WXYZ can be a parallelogram.
### Option 1:
"WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm."
- When one pair of sides is 15 mm and the other pair is 9 mm, both pairs of opposite sides are congruent.
- This configuration satisfies the condition for a parallelogram.
So, this option correctly explains that WXYZ can indeed be a parallelogram.
### Option 2:
"WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm."
- When one pair of sides is 15 mm and the other pair is 7 mm, both pairs of opposite sides are congruent.
- This configuration also satisfies the condition for a parallelogram.
So, this option also correctly explains that WXYZ can be a parallelogram.
### 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."
- Having three different values for [tex]\( x \)[/tex] does not necessarily explain why WXYZ cannot be a parallelogram.
- This option does not provide a valid reason related to the properties of a parallelogram.
So, this statement is not a valid explanation.
### 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] required to make one pair of sides congruent does not make the other pair congruent, WXYZ cannot be a parallelogram.
- This explanation correctly indicates that WXYZ cannot be a parallelogram based on side congruency.
So, this option correctly explains why WXYZ cannot be a parallelogram.
### Conclusion:
The valid explanations are:
1. WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.
2. WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm.
3. 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.
These options satisfy the conditions or correctly explain the reason behind whether WXYZ can be a parallelogram.
