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?

A. X = 4; y=6
B. X = 4; y = 12
C. X = 8; y = 6
D. X = 8; y = 12

Answer 1

To prove that quadrilateral ABCD is a parallelogram, we need to show that opposite sides are parallel and congruent. In this case, we can use the properties of the diagonals. By setting up the ratio EC/BD = AE/BE and substituting the given values, we find that X = 4 and y = 12.

Step-by-step explanation:

To prove that quadrilateral ABCD is a parallelogram, we need to show that opposite sides are parallel and congruent. In this case, we can use the properties of the diagonals.

Since EC = 4 and BD = 12, we can set up the following ratio: EC/BD = AE/BE

Substituting the given values, we have 4/12 = x/y

Simplifying this ratio, we get 1/3 = x/y

Therefore, the values of x and y that prove that the quadrilateral is a parallelogram are x = 4 and y = 12. So, the answer is X = 4; y = 12.