Question

For what value of x must ABCD be a parallelogram?

Justify your reasoning with theorems/postulates and show all work to receive credit.

Answer 1

Explanation:

Parallelogram's diagonals theorem states that the diagonals in a parallelogram must bisect each other.

So for ABCD to be a parallelogram, the two diagonals must be divided in equal sections.

That is given for BD already.

For AC, 3x = 4x - 6

Rearranging, 4x - 3x = 6

x = 6

Answer 2

Here is your answer

`\bold{x= 6}`

REASON:

Theorem used: The diagonals of a parallelogram bisect each other.

Let diagonals AC and BD bisect each other at O

So, OA=OC

Now,

3x=4x-6 [OA=3x and OC=4x-6]

4x-3x= 6

x= 6

HOPE IT IS USEFUL