Question

AB = 4x DC = 16 AD = y + 4 BC = 2y Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs.

Answer 1

To show that quadrilateral ABCD is a parallelogram, we need to find the lengths of the opposite side pairs. By equating the expressions for AB and DC, and AD and BC, we can solve for the values of x and y. Using x = 4 and y = 4, we can conclude that quadrilateral ABCD is a parallelogram.

Step-by-step explanation:

Given that AB = 4x, DC = 16, AD = y + 4, and BC = 2y, we need to show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs.

Opposite sides of a parallelogram are congruent. Therefore, AB = DC and AD = BC.

From AB = DC, we can equate the expressions: 4x = 16. Solving for x, we find that x = 4.

From AD = BC, we can equate the expressions: y + 4 = 2y. Solving for y, we find that y = 4.

So, we have found the values of x and y that make the opposite sides of quadrilateral ABCD congruent. Therefore, quadrilateral ABCD is a parallelogram.

Answer 2

Quadrilateral ABCD is a parallelogram when value of x is 4 and y is 4.

Step-by-step explanation:

Given:

Length of AB =
`4x`

Length of DC = 16

Length of AD =
`y+4`

Length of BC =
`2y`

Also Given:

In quadrilateral ABCD, we can say opposite sides are AB and DC and other Opposite sides are BC and AD.

hence we can check both for both equality

Length AB = Length of DC

Substituting the values we get;

`4x=16\\\\x=(16)/(4)=4`

when x=4

Length of AB =
`4x=4*4 =16` which is equal to Length of DC

Also for other pair;

Length BC = Length of AD

Substituting the values we get;

`y+4=2y\\\\2y-y = 4\\\\y= 4`

Hence Length of AD =
`y+4= 4+4 =8`

Length of BC =
`2y = 2* 4 =8`

Hence Length of AD = Length of BC

Since both pairs of opposite sides are congruent.

Hence, Quadrilateral ABCD is a parallelogram when value of x is 4 and y is 4.