Question

prove the consecutive interior angles theorem. drag the correct responses into the boxes to complete the proof. statements reasons 1. line a is parallel to line b. 1. given 2. 2. linear pairs theorem 3. ∠2 = ∠6 3. corresponding angles postulate 4. 4. congruent supplements theorem

Explanation:

Step1: Recall Linear Pairs Theorem

$\angle2$ and $\angle3$ form a linear - pair, so $\angle2+\angle3 = 180^{\circ}$

Step2: Use Corresponding Angles Postulate

Since $a\parallel b$, by the Corresponding Angles Postulate, $\angle2\cong\angle6$

Step3: Apply Congruent Supplements Theorem

Since $\angle2+\angle3 = 180^{\circ}$ and $\angle2\cong\angle6$, then $\angle6+\angle3 = 180^{\circ}$ (by the Congruent Supplements Theorem)

Answer:

1. $\angle2+\angle3 = 180^{\circ}$
2. $\angle6+\angle3 = 180^{\circ}$