Question

1. what is the value of x?

x - 2
4
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 (a segment connecting the midpoints of two sides) is half the length of the third side.
Let the mid - segment length be \(4\), and the length of the third side be \(x - 2\). According to the mid - segment theorem, 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 \(2\):
\(2\times4=x - 2\), which simplifies to \(8=x - 2\).
Add \(2\) to both sides of the equation: \(x=8 + 2\).

Answer:

\(x = 6\)