Question

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

Explanation:

Step1: Recall segment - addition postulate

The segment - addition postulate states that if we have three collinear points \(A\), \(B\), and \(C\) with \(B\) between \(A\) and \(C\), then \(AB + BC=AC\).

Step2: Analyze each option

• For the option \(AW + ES=AS\), points \(W\) and \(E\) are not on the same line segment between \(A\) and \(S\), so this is incorrect.
• For the option \(KT+TA = KA\), points \(K\), \(T\), and \(A\) are collinear and \(T\) is between \(K\) and \(A\). By the segment - addition postulate, \(KT + TA=KA\).
• For the option \(RU+UC = RC\), points \(R\), \(U\), and \(C\) are not collinear, so this is incorrect.
• For the option \(SR+UR = SK\), points \(S\), \(R\), \(U\), and \(K\) do not follow the correct collinear relationship for the segment - addition postulate, so this is incorrect.

Answer:

\(KT + TA=KA\)