Question

consider the image shown
which equation is true based on the lines in the diagram?
○ aw + es = as
○ rt + ta = ka
○ ru + uc = rc
○ sr + ur = sr

Explanation:

Step1: Analyze the line - segment addition postulate

The line - segment addition postulate states that if three points \(X\), \(Y\), and \(Z\) are collinear and \(Y\) is between \(X\) and \(Z\), then \(XY + YZ=XZ\).

Step2: Check each option

• Option 1: \(AW + ES=AS\)

Points \(W\) and \(E\) are not on the same line segment \(AS\). So, \(AW + ES
eq AS\).

• Option 2: \(RT+TA = KA\)

Points \(R\), \(T\), and \(A\) are not collinear. So, \(RT + TA
eq KA\).

• Option 3: \(RU+UC = RC\)

Points \(R\), \(U\), and \(C\) are collinear and \(U\) is between \(R\) and \(C\). By the line - segment addition postulate, if \(U\) lies on the line segment \(RC\), then \(RU+UC = RC\).

• Option 4: \(SR+UR = SK\)

Points \(S\), \(R\), \(U\), and \(K\) are not arranged in a way that \(SR + UR\) would equal \(SK\). Points \(U\) is not on the line segment \(SK\) in the correct order for the addition postulate.

Answer:

\(RU + UC=RC\)