Question

consider the figure. which reason can be used to justify statement 2? given: ( overline{ce} = overline{ed} ); ( overline{eb} cong overline{ce} ); ( e ) is the midpoint of ( overline{ab} ). prove: ( overline{ae} cong overline{ed} ). figure of intersecting lines with points a, c, b, d and intersection e statements: 1. ( overline{ce} = overline{ed} ); ( overline{eb} cong overline{ce} ); ( e ) is the midpoint of ( overline{ab} ). 2. ( overline{ae} cong overline{eb} ) 3. ( overline{ce} cong overline{ed} ) 4. ( overline{ae} cong overline{ce} ) 5. ( overline{ae} cong overline{ed} ) reasons: 1. given 2.? 3.? 4.? 5.?

Explanation:

Step1: Recall Midpoint Definition

A midpoint of a segment divides it into two congruent segments. Given \( E \) is the midpoint of \( \overline{AB} \), by the definition of a midpoint, the midpoint \( E \) splits \( \overline{AB} \) such that \( \overline{AE} \cong \overline{EB} \).

Step2: Identify Reason for Statement 2

Statement 2 is \( \overline{AE} \cong \overline{EB} \). The reason for this is the definition of a midpoint, which states that if a point is the midpoint of a segment, it divides the segment into two congruent parts. Since \( E \) is given as the midpoint of \( \overline{AB} \), this definition justifies \( \overline{AE} \cong \overline{EB} \).

Answer:

The reason to justify statement 2 (\( \overline{AE} \cong \overline{EB} \)) is the Definition of a Midpoint (a midpoint of a segment divides the segment into two congruent segments).