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 equality

If $\overline{RT}\cong\overline{WX}$, then $RT = WX$ (congruent segments have equal lengths). Adding the same segment length $TW$ to both sides of the equation $RT = WX$ still keeps the equation true according to the addition - property of equality.

Step2: Analyze each option

• Option 1: Since $RT = WX$, adding $TW$ to both sides gives $RT + TW=WX + TW$. This is a correct application of the addition - property of equality.
• Option 2: There is no information given to suggest that $RT = 2(RX)$.
• Option 3: There is no information given to suggest that $WX = 2(RX)$.
• Option 4: There is no information given to suggest that $RT + TW=RX$.

Answer:

RT + TW = WX + TW