Question

ux is a midsegment of \\( \triangle tvw \\).
if \\( vw = s + 23 \\) and \\( ux = s \\), what is the value of \\( s \\)?

Explanation:

Step1: Recall the midsegment theorem

The midsegment of a triangle is parallel to the third side and half its length. So \( VW = 2\times UX \).

Step2: Substitute the given expressions

Given \( VW=s + 23 \) and \( UX = s \), we substitute into the equation \( s+23=2s \).

Step3: Solve for \( s \)

Subtract \( s \) from both sides of the equation \( s+23 - s=2s - s \).

Answer:

\( s = 23 \)