Question

what can you conclude from the given information? state the reason for your conclusion. 1. ∠1≅∠2 2. n⊥m 3. (overrightarrow{ba}perpoverrightarrow{bc})

Explanation:

Step1: Analyze ∠1≅∠2

Vertical - angles are congruent. Since ∠1 and ∠2 are vertical - angles formed by the intersection of lines r and s, we can conclude that they are congruent.

Step2: Analyze n⊥m

When two lines are perpendicular, the angles formed at their intersection are right - angles. So, ∠1 = ∠2=∠3 = ∠4 = 90° because perpendicular lines form four right - angles.

Step3: Analyze $\overrightarrow{BA}\perp\overrightarrow{BC}$

Since $\overrightarrow{BA}\perp\overrightarrow{BC}$, then ∠ABC = 90° by the definition of perpendicular lines (perpendicular lines form right - angles).

Answer:

1. Conclusion: ∠1 and ∠2 are vertical angles and are congruent. Reason: Vertical angles are congruent.
2. Conclusion: ∠1 = ∠2=∠3 = ∠4 = 90°. Reason: Perpendicular lines form right - angles.
3. Conclusion: ∠ABC = 90°. Reason: Perpendicular lines form right - angles.