Question

given ( ab = cd )( cp = eb )prove ( ae = fd )what is the missing reason in the proof?a. segment additionb. congruent segments theoremc. transitive property of equalityd. subtraction property of equality

Explanation:

• Segment Addition Postulate: States that if \(A\), \(B\), and \(C\) are collinear points and \(B\) is between \(A\) and \(C\), then \(AB + BC=AC\). In the proof, \(AB = AC+CB\) and \(CD = CP + PD\) are applications of this postulate.
• Congruent Segments Theorem: Not relevant here as the key step is about segment addition.
• Transitive Property of Equality: States if \(a = b\) and \(b = c\), then \(a = c\). Not used in the segment - addition - based steps.
• Subtraction Property of Equality: States if \(a=b\), then \(a - c=b - c\). Not the basis for \(AB = AC + CB\) and \(CD = CP + PD\) steps.

Answer:

A. segment addition