Question

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

Answer 1

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:

`\begin{gathered} AB=CD \\ 2x+55=3x+35 \\ 55-35=3x-2x \\ x=20 \end{gathered}`

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

`\begin{gathered} AD=BC \\ 40+(x)/(2)=3x-10 \\ 40+10=3x-(x)/(2) \\ 50=(6x-x)/(2) \\ 50=(5x)/(2) \\ 5x=100 \\ x=(100)/(5) \\ x=20 \end{gathered}`

Thus, the x value is equal to 20.

Quadrilateral ABCD is a parallelogram.