Question

1. critique reasoning in a proof, alex wrote the following step: ab = 7 and bc = 7, so $overline{ab}congoverline{bc}$. transitive property of congruence. explain the error in alexs proof. then write the statements and reasons needed to get from ab = 7 and bc = 7 to $overline{ab}congoverline{bc}$.

Explanation:

Step1: Identify the error

Alex misused the Transitive Property. The Transitive Property is for congruence between three congruent objects like if \(A\cong B\) and \(B\cong C\) then \(A\cong C\). Here we are going from equality of lengths to congruence of segments.

Step2: Correct reasoning

If two segments have equal lengths, they are congruent by the definition of congruent segments.

Answer:

The error is that Alex misused the Transitive Property of Congruence.
Statements and Reasons:
Statement 1: \(AB = 7\) and \(BC=7\)
Reason 1: Given
Statement 2: \(\overline{AB}\cong\overline{BC}\)
Reason 2: Definition of congruent segments (If two segments have the same length, they are congruent)