Question

given that ( overline{rt} cong overline{wx} ), which statement must be true?
( \bigcirc rt + tw = wx + tw )
( \bigcirc rt = 2(rx) )
( \bigcirc wx = 2(rx) )
( \bigcirc 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 \(1 - 2\) ratio).
• There is no information to support \(RT + TW=RX\) (no geometric relationship given to make this equality hold).

Answer:

\(RT + TW=WX + TW\) (the first option)