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.
(4 points)
In order for ABCD to be a parallelogram, the opposite sides must be equal.
AE = CD, so we can set up the equation:
3x - 6 = 2x + 2
Subtract 2x from both sides:
x - 6 = 2
Add 6 to both sides:
x = 8
Now we can find the value of y.
DE = AB, so we can set up the equation:
6y - 12 = 2y + 24
Subtract 2y from both sides:
4y - 12 = 24
Add 12 to both sides:
4y = 36
Divide both sides by 4:
y = 9
Therefore, the values of x and y that make ABCD a parallelogram are x = 8 and y = 9.