Find the value of z. Then find GE and EH and state whether E is the midpoint of line GH. GH = z + 6. EH =2z-4. GE=z.
To find the value of z, we need to set up an equation based on the given information.
We are given that GE = z, GH = z + 6, and EH = 2z - 4.
Since E is the midpoint of line GH, it means that GE = EH. Therefore, z should be equal to 2z - 4.
Now, let's solve for z:
z = 2z - 4
Let's simplify the equation by subtracting z from both sides:
0 = z - 4
To isolate z, we add 4 to both sides:
4 = z
Thus, the value of z is 4.
Now that we know the value of z, we can find GE and EH.
GE = z = 4
EH = 2z - 4 = 2(4) - 4 = 8 - 4 = 4
As we can see, GE is equal to EH, which means that E is indeed the midpoint of line GH.