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Practice proving that a quadrilateral is a parallelogram.

In quadrilateral WXYZ, [tex]WC = 2x + 5[/tex] and [tex]CY = 3x + 2[/tex].

What must x equal for quadrilateral WXYZ to be a parallelogram?

Answer :

To determine what [tex]\( x \)[/tex] must equal for quadrilateral WXYZ to be a parallelogram, we need to use the property that in a parallelogram, opposite sides are equal.

Here's a step-by-step solution:

1. Given that in quadrilateral WXYZ, [tex]\( WC = 2x + 5 \)[/tex] and [tex]\( CY = 3x + 2 \)[/tex].
2. Since WXYZ is a parallelogram, opposite sides WC and CY must be equal, so we set the expressions for these sides equal to each other:
[tex]\[
2x + 5 = 3x + 2
\][/tex]
3. To solve for [tex]\( x \)[/tex], first subtract [tex]\( 2x \)[/tex] from both sides of the equation:
[tex]\[
5 = x + 2
\][/tex]
4. Next, subtract 2 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
3 = x
\][/tex]

Therefore, for quadrilateral WXYZ to be a parallelogram, [tex]\( x \)[/tex] must equal 3.

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