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. (4 points)
In a parallelogram, opposite sides are equal. Therefore, AE = CD and DE = BC.
We have AE = 3x-6 and CD = EC = 2x+2.
Setting these two expressions equal to each other, we have:
3x-6 = 2x+2
Combining like terms, we get:
x = 8
Next, we have DE = 6y-12 and BC = EB = 2y+24.
Setting these two expressions equal to each other, we have:
6y-12 = 2y+24
Combining like terms, we get:
4y = 36
Dividing both sides by 4, we get:
y = 9
Therefore, x = 8 and y = 9.