Question

AB = 3 + x

DC = 4x

AD = y + 1

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.

A) 4, 2

B) 4, 3

C) 6, 2

D) 6, 3

Answer 1

Option A) 4, 2

Explanation:

We are given that quadrilateral ABCD is a parallelogram with sides:

`AB = 3 + x\\DC = 4x\\AD = y + 1\\BC = 2y`

Since the opposite sides of a parallelogram are equal, we can write:

`AB = DC\\AD=BC`

Equating the sides we get,

`\Rightarrow 3+x = 4x\\4x-x = 3\\3x = 3\\x = 1\\\Rightarrow y + 1 = 2y\\y = 1`

Putting the values of x and y, we get:

`AB = 3 + x =4\\DC = 4x =4\\AD = y + 1=2\\BC = 2y=2`

Thus, the lengths of the opposite side pairs is 4,2.