Question

below is a proof of the alternate interior angle theorem: prove ∠1≅∠3. which of the following best completes the missing statement? step statement reason 1 m || n given 2 corresponding angles postulate 3 ∠2≅∠3 vertical angle theorem 4 ∠1≅∠3 substitution show your work here o ∠1≅∠2 o m∠1 + m∠4 = 180° o ∠3≅∠4 o ∠1≅∠4

Explanation:

Step1: Recall angle - related theorems

We know that to prove $\angle1\cong\angle3$ using the given steps, we need an angle - congruence relation that can be used for substitution.

Step2: Analyze the figure and steps

Since $m\parallel n$ (given), by the Corresponding Angles Postulate, we can get some angle - congruence relations. Also, we know $\angle2\cong\angle3$ by the Vertical Angle Theorem. To use substitution to get $\angle1\cong\angle3$, we need $\angle1\cong\angle2$.

Answer:

$\angle1\cong\angle2$