Given: Line segment AD bisects angle BAC. Angle 1 is congruent to angle 3.
Prove: Angle 2 is congruent to angle 3
Write a two-column proof
To prove that angle 2 is congruent to angle 3 using a two-column proof, we can use the information given and relevant angle pairs in a proof. Here's the step-by-step explanation:
**Statement** **Reason**
1. AD bisects angle BAC Given
2. Angle 1 is congruent to angle 3 Given
3. Angle 1 and angle 2 are supplementary Definition of a linear pair
4. Angle 3 and angle 2 are supplementary Definition of a linear pair
5. Angle 1 is congruent to angle 2 Substitution (from statement 3)
6. Angle 2 is congruent to angle 1 Symmetric property of equality
7. Angle 2 is congruent to angle 3 Transitive property of equality
Therefore, angle 2 is congruent to angle 3, which is proven using the given information and logical reasoning based on geometric definitions and properties.
Statement and reasons
m ے ABD = ½ m ے ABC