Which best explains if quadrilateral WXYZ can be a parallelogram?
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm.
WXYZ cannot be a parallelogram because there are three different values for [tex]$x$[/tex] when each expression is set equal to 15.
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.
Answer (1)
Parallelograms have congruent opposite sides.
Options 1 and 2 state conditions where WXYZ can be a parallelogram.
Option 4 explains that if the value of x making one pair of sides congruent doesn't make the other pair congruent, WXYZ cannot be a parallelogram.
Therefore, option 4 is the best explanation. WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.
Explanation
Understanding Parallelograms Let's analyze the properties of a parallelogram to determine which statement best explains if quadrilateral WXYZ can be a parallelogram. A key property of parallelograms is that their opposite sides must be congruent (equal in length).
Analyzing Each Option
Option 1: "WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm." This statement is true because if the opposite sides are equal, i.e., one pair is 15 mm each and the other pair is 9 mm each, then it can 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." Similar to option 1, this is also true if the opposite sides are equal (15 mm each and 7 mm each), then it can be a parallelogram.
Option 3: "WXYZ cannot be a parallelogram because there are three different values for x when each expression is set equal to 15." This statement introduces a variable x that is not defined in the problem, making it difficult to interpret without additional context. It suggests the side lengths might be defined in terms of x , but without knowing the expressions, we cannot evaluate this claim.
Option 4: "WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent." This statement also implies that the side lengths are defined in terms of x . If the value of x that makes one pair of opposite sides equal does not make the other pair of opposite sides equal, then WXYZ cannot be a parallelogram. This is because a parallelogram requires both pairs of opposite sides to be congruent.
Comparing the Options Options 1 and 2 are true but do not provide a definitive explanation of when WXYZ cannot be a parallelogram. They only state conditions under which it can be one. Options 3 and 4 introduce an undefined variable x , but option 4 provides a clearer condition for when WXYZ cannot be a parallelogram.
Conclusion Assuming the sides of WXYZ are defined in terms of x , option 4 provides the best explanation: If the value of x that makes one pair of sides congruent does not make the other pair of sides congruent, then WXYZ cannot be a parallelogram.
Examples
In architecture, understanding parallelograms is crucial for designing stable and aesthetically pleasing structures. For example, when designing a bridge with parallelogram-shaped supports, engineers must ensure that the opposite sides are perfectly congruent. If the sides are not congruent, the structure may be unstable and prone to collapse. This principle ensures structural integrity and safety in various engineering applications.
