9. construct arguments prove the consecutive interior angles theorem. given: p || q prove: ∠1 and ∠3 are…
9. construct arguments prove the consecutive interior angles theorem. given: p || q prove: ∠1 and ∠3 are supplementary.
Answer
Explanation:
Step1: Recall corresponding - angles property
Since (p\parallel q), (\angle1) and (\angle2) are corresponding angles. So, (\angle1=\angle2) (Corresponding - Angles Postulate).
Step2: Note linear - pair relationship
(\angle2) and (\angle3) form a linear pair. By the Linear - Pair Postulate, (\angle2+\angle3 = 180^{\circ}).
Step3: Substitute (\angle1) for (\angle2)
Since (\angle1=\angle2), we can substitute (\angle1) into the equation (\angle2+\angle3 = 180^{\circ}). We get (\angle1+\angle3 = 180^{\circ}).
Answer:
Since (\angle1+\angle3 = 180^{\circ}), (\angle1) and (\angle3) are supplementary.