This theorem is used to prove that 'm' is parallel to 'n' given that angles '1' and '2' are corresponding angles and are equal. therefore, option E is correct
Based on the second image which appears to show two lines marked as '1' and '2' intersecting two other lines labeled 'r' and 's', and the information that 'r' and 's' are parallel lines, we can infer the relationship between 'm' and 'n'.
If angle '1' is formed by the intersection of line 'm' with line 'r' and angle '2' is formed by the intersection of line 'n' with line 's', and these angles are marked, they are likely corresponding angles. When a transversal crosses two parallel lines, corresponding angles are equal.
Therefore, if angles '1' and '2' are corresponding angles and are marked to indicate they are equal, then by the Corresponding Angles Postulate, line 'm' is parallel to line 'n'.
The Corresponding Angles Postulate states that if a transversal intersects two parallel lines, then each pair of corresponding angles is congruent. The converse of this postulate is also true: if two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.
So, from the given choices, the correct theorem to use would be:
Yes. Corresponding Angles Converse
This theorem is used to prove that 'm' is parallel to 'n' given that angles '1' and '2' are corresponding angles and are equal.