Question

1. tw is a midsegment of auv.4) if uv = x + 4 and tw = x + 6, what is the value of x?x =

Explanation:

Step1: Use the mid - segment theorem

Since \(TW\) is a mid - segment of \(\triangle UVB\), by the mid - segment theorem, \(TW=\frac{1}{2}UB\).
Given \(UB = 14\) and \(TW=x + 6\).
So, \(x + 6=\frac{1}{2}\times14\).

Step2: Solve the equation

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times14 = 7\).
Then, solve \(x+6 = 7\) for \(x\). Subtract \(6\) from both sides of the equation: \(x=7 - 6\).

Answer:

\(x = 1\)