Question

problem 13: (first taught in lesson 44) from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: a - d - s; prove: ad < as

Explanation:

Step1: Understand the segment - addition postulate

The segment - addition postulate states that if \(A - D - S\) (points \(A\), \(D\), and \(S\) are collinear with \(D\) between \(A\) and \(S\)), then \(AS=AD + DS\).

Step2: Analyze the relationship between \(AD\) and \(AS\)

Since \(DS>0\) (a non - zero length of a segment), from \(AS = AD+DS\), we can rewrite the equation as \(AD=AS - DS\).

Answer:

The segment - addition postulate.