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.

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

Step-by-step 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  

For 'y' i.e BC = AD

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

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

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

move it to the other side

step-by-step explanation: