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Practice proving that a quadrilateral is a parallelogram.

In quadrilateral [tex]WXYZ[/tex], [tex]WC = 2x + 5[/tex] and [tex]CY = 3x + 2[/tex]. What must [tex]x[/tex] equal for quadrilateral [tex]WXYZ[/tex] to be a parallelogram?

[tex]x = \square[/tex]

Answer :

To prove that quadrilateral [tex]\(WXYZ\)[/tex] is a parallelogram, we need to ensure that its opposite sides are equal. In this case, we are looking at sides [tex]\(WC\)[/tex] and [tex]\(CY\)[/tex].

We are given:
- [tex]\(WC = 2x + 5\)[/tex]
- [tex]\(CY = 3x + 2\)[/tex]

Since these two sides must be equal for [tex]\(WXYZ\)[/tex] to be a parallelogram, we set the expressions for [tex]\(WC\)[/tex] and [tex]\(CY\)[/tex] equal to each other:

[tex]\[
2x + 5 = 3x + 2
\][/tex]

Now, let's solve for [tex]\(x\)[/tex]:

1. Subtract [tex]\(2x\)[/tex] from both sides of the equation to get the terms with [tex]\(x\)[/tex] on one side:

[tex]\[
5 = x + 2
\][/tex]

2. Subtract 2 from both sides to solve for [tex]\(x\)[/tex]:

[tex]\[
5 - 2 = x
\][/tex]

[tex]\[
3 = x
\][/tex]

So, for quadrilateral [tex]\(WXYZ\)[/tex] to be a parallelogram, [tex]\(x\)[/tex] must equal 3. This ensures that the opposing sides are equal, satisfying the conditions for a parallelogram.

Thanks for taking the time to read Practice proving that a quadrilateral is a parallelogram In quadrilateral tex WXYZ tex tex WC 2x 5 tex and tex CY 3x 2 tex What. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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