Question

Given ∠8≅∠12, which lines, if any, must be parallel based on the given information? Justify your conclusion.

Answer 1

Did you figure this out yet???

Answer 2

Answer: $a\parallel b$, converse of corresponding angles theorem.

Explanation: Since, according to the corresponding angle theorem if two lines are parallel and they are cut by the same transversal then the pair of corresponding angles must be equal.

The converse of the theorem also exists, which is, if the corresponding angles   in two lines by the same transversal are equal then these lines must be parallel.

Here, $\angle 8$ and $\angle 12$ are equal and they are made on line a and b respectively by common transversal c.

Therefore, according to the converse of corresponding angles theorem

$a\parallel b$