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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 determine the value of [tex]\( x \)[/tex] that makes quadrilateral [tex]\( WXYZ \)[/tex] a parallelogram, we need to remember that in a parallelogram, opposite sides are equal. Here, we're given [tex]\( WC = 2x + 5 \)[/tex] and [tex]\( CY = 3x + 2 \)[/tex]. To make [tex]\( WXYZ \)[/tex] a parallelogram, we need these two sides to be equal because [tex]\( WC \)[/tex] and [tex]\( CY \)[/tex] are opposite sides.

The equation for this scenario will be:

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

Let's solve this equation step by step:

1. Subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[ 2x + 5 - 2x = 3x + 2 - 2x \][/tex]
[tex]\[ 5 = x + 2 \][/tex]

2. Subtract 2 from both sides:
[tex]\[ 5 - 2 = x + 2 - 2 \][/tex]
[tex]\[ 3 = x \][/tex]

Therefore, the value of [tex]\( x \)[/tex] that ensures the quadrilateral [tex]\( WXYZ \)[/tex] is a parallelogram is [tex]\( x = 3 \)[/tex].

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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