Given ∠1≅∠7, which lines, if any, must be parallel based on the given information? justify your conclusion. a∥b, converse of the corresponding angles theorem c∥d, converse of the alternate exterior angles theorem a∥b, converse of the same-side interior angles theorem not enough information to make a conclusion

Since we know that  ∠1≅∠7, therefore, lines c and d are parallel lines based on the Converse of the Alternate Exterior Angles Theorem. The correct answer will be: c∥d, Converse of the Alternate Exterior Angles Theorem

Referring to the image given, we are told that  ∠1≅∠7.

∠1 and ∠7 lie on opposite sides of the transversal line b.

The transversal line cuts across line c and d.

∠1 and ∠7 are exterior angles because they lie outside lines c and d.

Based on the alternate exterior angles theorem, two alternate exterior angles are congruent if two lines that they lie on are parallel.

Therefore, since we know that  ∠1≅∠7, therefore, lines c and d are parallel lines based on the Converse of the Alternate Exterior Angles Theorem. The correct answer will be: c∥d, Converse of the Alternate Exterior Angles Theorem

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c∥d, Converse of the Alternate Exterior Angles Theorem

Step-by-step explanation:

We know that the alternate exterior angles are angles that are on opposite sides of the transversal and are on outside the two lines.

From the given figure it is given that ∠1≅∠7, Hence, by converse of alternate exterior theorem c∥d.