Question

given that rt ≅ wx, which statement must be true?
o rt + tw = wx + tw
o rt = 2(rx)
o wx = 2(rx)
o rt + tw = rx

Explanation:

Step1: Use segment addition postulate

By segment addition postulate, \(RX = RT+TW\).

Step2: Use congruent segments property

Since \(RT\cong WX\), then \(RT = WX\). Substitute \(WX\) for \(RT\) in \(RX = RT + TW\), we get \(RX=WX + TW\).

Answer:

\(RT + TW=WX + TW\) (This is equivalent to the segment - addition - based relationship derived above. If we assume the options are presented in a way that the correct one is based on segment addition and congruence, and if we consider the standard multiple - choice setup where the correct answer is the one that follows from \(RT\cong WX\) (i.e., \(RT = WX\)) and \(RX=RT + TW\) (segment addition). If the options are:

• \(RT + TW=RX\) (segment addition, but no use of \(RT\cong WX\))
• \(WX = 2(RX)\) (not supported by given)
• \(RT=2(RX)\) (not supported by given)
• \(RT + TW=WX + TW\) (using \(RT = WX\) (from \(RT\cong WX\)) and \(RX = RT+TW\) (segment addition))

The answer is \(RT + TW=WX + TW\))