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The quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Given side lengths, prove that quadrilateral ABCD is a parallelogram by finding the value of x

The Quadrilateral ABCD Is A Parallelogram If Both Pairs Of Opposite Sides Are Congruent Given Side Lengths Prove That Quadrilateral ABCD Is A Parallelogram By F class=

Answer :

In parallelograms, opposite sides are equal in length.

There are 2 pair of parallel sides.

In parallelogram ABCD, the congruent sides are:

• AB = CD

and

• AD = BC

Let's equate AB = CD and solve for x:

[tex]\begin{gathered} AB=CD \\ 2x+55=3x+35 \\ 55-35=3x-2x \\ x=20 \end{gathered}[/tex]

Now, let's equate AD = BC and solve for x:

[tex]\begin{gathered} AD=BC \\ 40+\frac{x}{2}=3x-10 \\ 40+10=3x-\frac{x}{2} \\ 50=\frac{6x-x}{2} \\ 50=\frac{5x}{2} \\ 5x=100 \\ x=\frac{100}{5} \\ x=20 \end{gathered}[/tex]

Thus, the x value is equal to 20.

Quadrilateral ABCD is a parallelogram.

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