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

Answer:

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;

$4x=16\\\\x=\frac{16}{4}=4$

when x=4

Length of AB = $4x=4\times4 =16$ 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 = $2y = 2\times 4 =8$

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.