Answer:
To prove that angle 1 and angle 3 are congruent, given that angle 1 and angle 2 are congruent, you can use the following two-column proof:
Statements Reasons
1. angle 1 = angle 2 Given
2. angle 2 = angle 1 Symmetric Property of Equality
3. angle 1 = angle 3 Transitive Property of Equality
4. angle 1 ≅ angle 3 Definition of Congruent Angles
In this proof, the Symmetric Property of Equality is used to state that if angle 1 is equal to angle 2, then angle 2 is equal to angle 1. The Transitive Property of Equality is then used to state that if angle 2 is equal to angle 1 and angle 1 is equal to angle 3, then angle 2 is equal to angle 3. Finally, the Definition of Congruent Angles is used to conclude that angle 1 and angle 3 are congruent.
OR
Explanation:
- Given that angle 1 and angle 2 are congruent.
- Supplementary angles add up to 180 degrees. Since angle 2 is supplementary to angle 3, and angle 2 is congruent to angle 1, it implies that angle 1 and angle 3 are supplementary.
- Using the transitive property of equality, if angle 1 and angle 2 are congruent, and angle 2 and angle 3 are supplementary, then angle 1 and angle 3 are also supplementary.
- Using the subtraction property of equality, if two angles are supplementary to the same angle, then they are congruent to each other. Therefore, angle 1 and angle 3 are congruent.
Step-by-step explanation:
