Question

t is the midpoint of ux and v is the midpoint of uw. if tv = 20, what is wx? w v x t u wx =

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. In \(\triangle UWX\), since \(T\) is the midpoint of \(UX\) and \(V\) is the midpoint of \(UW\), then \(TV\) is the mid - segment of \(\triangle UWX\).

Step2: Relate \(TV\) and \(WX\)

According to the mid - segment theorem, \(TV=\frac{1}{2}WX\). Given \(TV = 20\).
We can solve for \(WX\) by multiplying both sides of the equation \(TV=\frac{1}{2}WX\) by \(2\). So \(WX=2\times TV\).
Substitute \(TV = 20\) into the equation: \(WX=2\times20\).

Answer:

\(40\)