Question

given: $overline{rw}$ and $overline{pk}$ intersect at point $s$ so that $rs = ps$ and $sw = sk$. prove: $rw = pk$. statements: 1. $overline{rw}$ and $overline{pk}$ intersect at point $s$ so that $rs = ps$ and $sw = sk$. 2. $rs + sw = ps + sk$. 3. $rs + sw = rw; ps + sk = pk$. 4. $rw = pk$. reasons: 1. given. 2. addition property. 3. 4. substitution property. what is the correct reason for statement 3? subtraction property. segment addition postulate. given. substitution property.

Explanation:

The Segment Addition Postulate states that if we have three collinear points \(A\), \(B\), and \(C\), then \(AB + BC=AC\). In the context of line - segments \(\overline{RW}\) and \(\overline{PK}\), since \(S\) lies on \(\overline{RW}\), \(RS + SW=RW\) and since \(S\) lies on \(\overline{PK}\), \(PS + SK = PK\).

Answer:

Segment Addition Postulate