Use the given plan to write a two-column proof of the Symmetric Property of Congruence.
Given: segment AB ≅ segment EF
Prove: segment EF ≅ segment AB
Plan: Use the definition of congruent segments to write segment AB ≅ segment EF as a statement of equality. Then use the Symmetric Property of Equality to show that EF=AB. So segment EF ≅ segment AB by the definition of congruent segments.
Statements Reasons
1. segment AB ≅ segment EF Given
2. AB = EF Definition of congruent segments
3. EF = AB Symmetric Property of Equality
4. segment EF ≅ segment AB Definition of congruent segments
To prove the Symmetric Property of Congruence, we will follow the given plan:
Given: segment AB ≅ segment EF
Prove: segment EF ≅ segment AB
Proof:
1. Segment AB ≅ Segment EF (Given)
2. AB = EF (Definition of congruent segments)
3. EF = AB (Symmetric Property of Equality, switching sides of the equation)
4. Segment EF ≅ Segment AB (Definition of congruent segments)
Thus, we have proved the Symmetric Property of Congruence using the given plan.