If AE=3x-6, DE = 6y-12, EC = 2x+2 and EB = 2y+24, find the values of x and y for which ABCD must be a parallelogram. The drawing is not to scale.
To determine when ABCD is a parallelogram, we need to show that both pairs of opposite sides are equal in length.
For this strategy, we will equate AE to EC, and DE to EB.
Setting AE = EC, we have 3x - 6 = 2x + 2.
Simplifying, we find x = 8.
Setting DE = EB, we have 6y - 12 = 2y + 24.
Simplifying, we find y = 6.
Therefore, when x = 8 and y = 6, ABCD is a parallelogram.