A conjecture and the two-column proof used to prove the conjecture are shown. Given: angle 1 is supplementary to angle 2. Ray B D bisects angle A B C. Prove: angle 1 is supplementary to angle 3. Ray B A and ray B C connected at point B form an angle labeled as A B C. A ray B D starts from point B, bisecting the angle A B C into two parts A B D and C B D. Angle A B D is labeled as 2 and angle C B D is labeled as 3. There is a separate angle labeled 1.

Drag an expression or phrase to each box to complete the proof.

Statement Reason
1. ∠1 is supplementary to ∠2. Given
2. Response area Definition of supplementary
3. BD−→− bisects ∠ABC. Given
4. m∠2=m∠3 Response area
5. Response area Response area
6. ∠1 is supplementary to ∠3. Definition of supplementary