Question

The diagonals of quadrilateral ABCD
intersect at E
. If EC=4, BD=12, AE=x,
and BE=y
, what values of x
and y
would prove that the quadrilateral is a parallelogram?

Answer 1

Answer:

Step-by-step explanation:

16 ae =x

Answer 2

The values of x

and y  that would prove that the quadrilateral is a parallelogram are 4 and 6 respectively.

Find the diagram attached. In order to prove that the quadrilateral is a parallelogram, we need to find the values of x and y that make the diagram a parallelogram.

From the parallelogram;

• AE = EC and BE = ED

• BD = BE + ED

• AC = AE + EC

Given the following parameters

EC=4,

BD=12,

Since AE = EC, hence the measure of AE is 4.

Similarly, BD = BE + ED

BD = BE + BE

BD = 2BE

12 = 2BE

BE = 6 = y

Hence the values of x

and y  that would prove that the quadrilateral is a parallelogram are 4 and 6 respectively.

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