determine the values of x and y for which ABCD is a parallelogram. AB = 3x + 7, BC = y +8, CD = 5x + 1, DA = 2y - 3
The opposite sides are equal:
AB = CD
3x + 7 = 5x + 1
3x - 5x = 1 - 7
-2x = -6
X = 3.
BC = DA
y + 8 = 2y - 3
y - 2y = -3 -8
-y = -11
Y = 11.
To determine the values of x and y for which ABCD is a parallelogram, we need to use the properties of parallelograms.
One property of parallelograms is that opposite sides are congruent. In other words, AB is congruent to CD and BC is congruent to DA.
Equating the corresponding sides, we have the following equations:
AB = CD : 3x + 7 = 5x + 1
BC = DA : y + 8 = 2y - 3
Let's solve these equations one by one.
For the equation 3x + 7 = 5x + 1, we can solve for x by isolating x on one side of the equation:
3x - 5x = 1 - 7
-2x = -6
x = -6 / -2
x = 3
Now, let's solve the equation y + 8 = 2y - 3 in the same manner:
-3 - 8 = 2y - y
-11 = y
Therefore, the values of x and y for which ABCD is a parallelogram are x = 3 and y = -11.