Question

given: ab = bc
bc = bd
prove: b is the mid - point of $overline{ad}$
statements: reasons:

1. ab = bc 1.

bc = bd

1. ab = bd 2.
2. b is the mid - point of ad 3.

Explanation:

Step1: Given information

Given \(AB = BC\) and \(BC = BD\)

Step2: Transitive property of equality

Since \(AB = BC\) and \(BC = BD\), by the transitive - property of equality (if \(a = b\) and \(b = c\), then \(a = c\)), we have \(AB=BD\)

Step3: Definition of mid - point

A point \(B\) is the mid - point of a line segment \(\overline{AD}\) if \(AB = BD\). Since \(AB = BD\), \(B\) is the mid - point of \(\overline{AD}\)

Answer:

1. Given
2. Transitive property of equality
3. Definition of mid - point