Question

What is the reason for Statement 4 of the two-column proof?

Statements Reasons
1. B is the midpoint of AC Given
2. AB¯¯¯¯¯≅BC¯¯¯¯¯ Definition of midpoint
3. BC¯¯¯¯¯≅DE¯¯¯¯¯ Given
4. AB¯¯¯¯¯≅DE¯¯¯¯¯ ?

-Transitive Property of Congruence
-Symmetric Property of Equality
-Segment Congruence Postulate
-Segment Addition Postulate

Answer 1

Refer to the given figure.

    Statements                                                Reasons

1. B is the midpoint of AC                                 Given

2. $AB \cong BC$                                  Definition of midpoint

3.  $BC \cong DE$                                 Given

4.  $AB \cong DE$                                Transitive property of congruence

The reason for statement 4 is " transitive property of congruence" which states that " If two segments (or angles) are each congruent to a third segment (or angle), then they're congruent to each other".

Answer 2

Answer:Refer to the given figure.

   Statements                                                Reasons

1. B is the midpoint of AC                                 Given

2.                                   Definition of midpoint

3.                                   Given

4.                                  Transitive property of congruence

The reason for statement 4 is " transitive property of congruence" which states that " If two segments (or angles) are each congruent to a third segment (or angle), then they're congruent to each other".

Step-by-step explanation: