Question

given that (overline{rt}congoverline{wx}), which statement must be true?
(rt + tw = wx + tw)
(rt = 2(rx))
(wx = 2(rx))
(rt + tw = rx)

Explanation:

Step1: Use the property of congruent segments

Since \(\overline{RT}\cong\overline{WX}\), then \(RT = WX\) (by the definition of congruent segments).

Step2: Apply the addition property of equality

If \(a = b\), then \(a + c=b + c\). Let \(a = RT\), \(b = WX\) and \(c=TW\).
So \(RT + TW=WX + TW\).

For the other options:

• There is no information given to suggest that \(RT = 2(RX)\) or \(WX = 2(RX)\) (no indication that \(RX\) is related to \(RT\) or \(WX\) in a \(2 - to - 1\) ratio).
• Also, there is no basis for \(RT + TW=RX\) as there is no geometric or algebraic relation provided to support this equality.

Answer:

\(RT + TW = WX + TW\)