in parallelogram DEFG, DH = x + 1, HF = 3y, GH = 3x – 4, and HE = 5y + 1. Find the values of x and y. The diagram is not drawn to scale.
In a parallelogram, opposite sides are congruent. Therefore, we have the following equations:
DH = FG ⟹ x + 1 = 3x – 4
HF = DE ⟹ 3y = 5y + 1
Let's solve the equations one by one:
From the first equation:
x + 1 = 3x – 4
4 + 1 = 3x – x
5 = 2x
x = 5/2
From the second equation:
3y = 5y + 1
3y - 5y = 1
-2y = 1
y = -1/2
Therefore, the values of x and y are 5/2 and -1/2, respectively.