Question

1. what is the value of x?

4
10
6
8

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment of a triangle is half the length of the parallel side. Here, the side with length \(4\) is the mid - segment and the side with length \(x - 2\) is the parallel side. So, we have the equation \(4=\frac{1}{2}(x - 2)\).

Step2: Solve the equation for \(x\)

Multiply both sides of the equation \(4=\frac{1}{2}(x - 2)\) by \(2\): \(4\times2=x - 2\), which simplifies to \(8=x - 2\).
Add \(2\) to both sides: \(x=8 + 2\).

Answer:

\(x = 10\)