Final answer:
By applying the properties of a parallelogram, the value of GE and DF are determined to be 5 each, after finding y = 7 and x = 1 from the given equations.
Step-by-step explanation:
In parallelogram DEFG, we are given that segment DH is equal to 2y + 6, segment HF equals 4x + 1, segment HE equals 3x + 2, and segment GH equals 20. To find the values of GE and DF, we need to use the properties of a parallelogram that opposite sides are equal. Since DH and GF are opposite sides of a parallelogram, they must be equal. The same applies to HE and DF.
We can set up the equations as follows:
- DH = GF ⇒ 2y + 6 = 20 ⇒ y = 7
- HE = DF ⇒ 3x + 2 = 4x + 1
By solving the first equation, we find that y = 7. Substituting the value of y into DH, we get GH = 2(7) + 6, which simplifies to GH = 20. For the second equation, solving for x gives us x = 1. Substituting x = 1 into HE, we get HE = 3(1) + 2, which equals 5. Therefore, GE and DF both equal 5.