Question

drag the correct reasons into the boxes to complete the proof. show hints statements reasons 1. line a is parallel to line b. 1. 2. ∠5 is supplementary to ∠2. 2. 3. ∠1 is supplementary to ∠2. 3. 4. ∠1≅∠5 4.

Explanation:

Step1: Given information

Given

Step2: Use corresponding - angle and linear - pair relationships

If two parallel lines are cut by a transversal, corresponding angles are congruent and linear - pair angles are supplementary. $\angle5$ and $\angle2$ are related as follows: $\angle5$ and $\angle6$ are a linear pair ($\angle5+\angle6 = 180^{\circ}$), and $\angle6\cong\angle2$ (corresponding angles for $a\parallel b$), so $\angle5$ is supplementary to $\angle2$.

Step3: Definition of linear - pair

$\angle1$ and $\angle2$ form a linear pair, so $\angle1$ is supplementary to $\angle2$ (by the definition of linear - pair, the sum of angles in a linear pair is $180^{\circ}$).

Step4: Congruent supplements theorem

If two angles are supplementary to the same angle, then they are congruent. Since $\angle1$ and $\angle5$ are both supplementary to $\angle2$, $\angle1\cong\angle5$.

Answer:

1. Given
2. Corresponding angles and linear - pair relationships
3. Definition of linear - pair
4. Congruent supplements theorem