Question

AB = 4x DC = x + 9 AD = 6 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

C) 12, 6

Set opposite sides equal to each other and solve for x or y.

AB = DC → 4x = x + 9 → 3x = 9 → x = 3

So, AB = DC = 12

And,

AD = BC → 6 = 2y → y = 3

So, AD = BC = 6

Answer 2

Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .

Explanation:

Given:

[] ABCD is a Parallelogram.

∴ pairs of opposite sides are congruent

∴ AB = DC and

BC = AD

To Find:

Length of AB = ?

Length of BC = ?

Solution:

[] ABCD is a Parallelogram. .............Given

∴ pairs of opposite sides are congruent

∴ AB = DC and BC = AD

On substituting the values we get

For 'x' i.e AB = DC

`4x=x+9\\\\4x-x=9\\\\3x=9\\\\x=(9)/(3)\\ \\x=3`

For 'y' i.e BC = AD

`2y=6\\\\y=(6)/(2) \\\\y=3\\`

Now substituting 'x' and 'y' in AB and BC we get,

`Length\ AB=4* 3 =12\ units\\\\Length\ BC=2* 3 =6\ units`

Therefore the lengths of the opposite side pairs, AB and BC are 12 units and 6 units .