Question

given: ∠1≅∠2 prove: a||b fill in the missing steps of the proof of the converse of the alternate interior angles theorem. drag and drop the correct choice into the drop areas on the image above. statements: 1) ∠1≅∠2 2) ∠2≅∠3 3) ∠1≅∠3 4) a||b reasons: 1) given 2) vertical angles theorem 3) 4)

Explanation:

Step1: Recall vertical - angles property

$\angle2\cong\angle4$ because vertical angles are congruent.

Step2: Use the given and transitive property

Given $\angle1\cong\angle2$, and since $\angle2\cong\angle4$, then $\angle1\cong\angle4$ by the transitive property of congruence.

Step3: Apply corresponding - angles postulate

If $\angle1\cong\angle4$, then $a\parallel b$ by the converse of the corresponding - angles postulate.

Answer:

1. $\angle2\cong\angle4$ (Vertical Angles Theorem)
2. $\angle1\cong\angle4$ (Transitive Property of Congruence, since $\angle1\cong\angle2$ and $\angle2\cong\angle4$)
3. $a\parallel b$ (Converse of the Corresponding Angles Postulate, since $\angle1$ and $\angle4$ are corresponding angles and $\angle1\cong\angle4$)