Question

prove the consecutive exterior angles theorem using the figure shown. drag the correct statements or reasons into the boxes to complete the proof. show hints statements reasons 1. line a is parallel to line b. 1. given 2. 2. 3. 3. corresponding angles postulate 4. ∠1 is supplementary to ∠6 4.

Explanation:

Step1: Identify corresponding angles

$\angle1$ and $\angle 5$ are corresponding angles. Since line $a\parallel b$, by the Corresponding Angles Postulate, $\angle1=\angle5$.

Step2: Consider linear - pair relationship

$\angle5$ and $\angle6$ form a linear - pair. By the Linear - Pair Postulate, $\angle5+\angle6 = 180^{\circ}$.

Step3: Substitute $\angle1$ for $\angle5$

Since $\angle1=\angle5$ and $\angle5+\angle6 = 180^{\circ}$, by substitution, $\angle1+\angle6 = 180^{\circ}$, which means $\angle1$ is supplementary to $\angle6$.

Answer:

1. Statements: $\angle1=\angle5$; Reasons: Corresponding Angles Postulate
2. Statements: $\angle5+\angle6 = 180^{\circ}$; Reasons: Linear - Pair Postulate
3. Statements: $\angle1+\angle6 = 180^{\circ}$; Reasons: Substitution Property of Equality